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Coordinate Geometry
Coordinate GeometryDistance Formula
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
The distance formula is finding the length of the hypotenuse,
using Pythagoras
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Midpoint Formula
The distance formula is finding the length of the hypotenuse,
using Pythagoras
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Midpoint Formula
1 2 1 2,2 2
x x y yM
The distance formula is finding the length of the hypotenuse,
using Pythagoras
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Midpoint Formula
1 2 1 2,2 2
x x y yM
e.g. Find the midpoint of (3,4) and (–2 ,1)
The distance formula is finding the length of the hypotenuse,
using Pythagoras
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Midpoint Formula
1 2 1 2,2 2
x x y yM
e.g. Find the midpoint of (3,4) and (–2 ,1)
3 2 4 1,2 2
M
The distance formula is finding the length of the hypotenuse,
using Pythagoras
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Midpoint Formula
1 2 1 2,2 2
x x y yM
e.g. Find the midpoint of (3,4) and (–2 ,1)
3 2 4 1,2 2
M
1 5,2 2
The distance formula is finding the length of the hypotenuse,
using Pythagoras
Coordinate GeometryDistance Formula
2 22 1 2 1d x x y y
e.g. Find the distance between (–1,3) and (3,5)
2 25 3 3 1d
2 22 4
20
2 5 units
Midpoint Formula
1 2 1 2,2 2
x x y yM
e.g. Find the midpoint of (3,4) and (–2 ,1)
3 2 4 1,2 2
M
1 5,2 2
The distance formula is finding the length of the hypotenuse,
using Pythagoras
The midpoint formula averages the x and y values
Division Of An Interval
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X Y
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
A divides XY internally in the ratio m:n
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
A divides XY internally in the ratio m:n
m
n
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
A divides XY internally in the ratio m:n
m
n
OR
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
A divides XY internally in the ratio m:n
m
n
ORA divides YX internally in the ratio n:m
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
X Y
A divides XY internally in the ratio m:n
m
n
ORA divides YX internally in the ratio n:m
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
X Y A
A divides XY internally in the ratio m:n
m
n
ORA divides YX internally in the ratio n:m
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
X Y A
A divides XY internally in the ratio m:n
m
n
ORA divides YX internally in the ratio n:m
A divides XY externally in the ratio m:n
Division Of An IntervalMathematics (2 unit) division of an interval questions are restricted to midpoint questions i.e. dividing in the ratio 1:1
In Extension 1 you can be asked to divide an interval in a any ratio, and it could be either an internal or an external division.
X YA
X Y A
A divides XY internally in the ratio m:n
m
n
ORA divides YX internally in the ratio n:m
A divides XY externally in the ratio m:n
m
n
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
4 4
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
4 4
• Multiply along the cross and add to get the numerator
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
4 4
• Multiply along the cross and add to get the numerator5133
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
4 4
• Multiply along the cross and add to get the numerator5133 6143
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
4 4
• Multiply along the cross and add to get the numerator5133 6143
418,
44
Type 1: Internal Division
Find the coordinates of P that divides the interval joining and internally in the ratio 1 : 3
4,3
2003 Extension 1 HSC Q1c)
6,5• Write down the endpoints of the interval in the same order as
they are mentioned.
4,3 6,5
• Write down the ratio.
3:1
• Draw a cross joining the ratio to the two points• Set up your answer by drawing a set of parentheses with two
vinculums separated by a comma
, P
• Add the numbers in the ratio together to get the denominator
4 4
• Multiply along the cross and add to get the numerator5133 6143
418,
44
29,1
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
, P
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
, P 3 3
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
, P 3 39532
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
, P 3 39532 2512
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
, P 3 39532 2512
3
12,3
39
Type 2: External Division
Let A be the point and B be the point . Find the coordinates of the point P which divides AB externally in the ratio 5 : 2.
1,3
2004 Extension 1 HSC Q1c)
2,9
• Done exactly the same as internal division, except make one of the numbers in the ratio negative
1,3 2,9
2:5
, P 3 39532 2512
3
12,3
39
4,13
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A yxB ,
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
yxB ,
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
yxB ,
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:2
yxB ,
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:2
yxB ,
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:2
yxB ,
• Create the fraction for the x value and equate it with the known value
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
yxB ,
• Create the fraction for the x value and equate it with the known value
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
yxB ,
• Create the fraction for the x value and equate it with the known value
x235
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
yxB ,
• Create the fraction for the x value and equate it with the known value
x235
482
xx
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
yxB ,
• Create the fraction for the x value and equate it with the known value• Repeat for the y value
x235
482
xx
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
52834 y
yxB ,
• Create the fraction for the x value and equate it with the known value• Repeat for the y value
x235
482
xx
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
52834 y
yxB ,
• Create the fraction for the x value and equate it with the known value• Repeat for the y value
x235
482
xx
y22420
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
52834 y
yxB ,
• Create the fraction for the x value and equate it with the known value• Repeat for the y value
x235
482
xx
y22420
242
yy
Type 3: Find an endpoint of an interval
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P
2005 Extension 1 HSC Q1e)
8,1A
• Draw the endpoints, ratio and cross the same as previously
8,1 yx,
3:25
2131 x
52834 y
2,4 B
yxB ,
• Create the fraction for the x value and equate it with the known value• Repeat for the y value
x235
482
xx
y22420
242
yy
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A B
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
, B
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
, B2 2
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
, B2 2
1513
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
, B2 2
1513 4583
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
, B2 2
1513 4583
2
4,28
Alternative
The point divides the line segment joining and internally in the ratio 2 : 3.
Find the coordinates of the point B.
4,1P 8,1A yxB ,
A BP 3
2
If P divides AB internally in the ratio 2 : 3
Then B divides AP externally in the ratio 5 : 3
8,1 4,1
3:5
, B2 2
1513 4583
2
4,28
2,4
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6 4,0
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,0
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
4,0
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
4,0
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
4,0
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
4,0
• Create the fraction for the either the x value or the y value (it does not matter which one) and equate it with the known value
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
10613
k
k
4,0
• Create the fraction for the either the x value or the y value (it does not matter which one) and equate it with the known value
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
10613
k
k
4,0
• Create the fraction for the either the x value or the y value (it does not matter which one) and equate it with the known value
633 k
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
10613
k
k
4,0
• Create the fraction for the either the x value or the y value (it does not matter which one) and equate it with the known value
633 k
393
kk
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
10613
k
k
1:3ratioin theexternally divides ABP
4,0
• Create the fraction for the either the x value or the y value (it does not matter which one) and equate it with the known value
633 k
393
kk
Type 4: Finding the ratio
The point divides the interval externally in the ratio k : 1.
If A is the point and B is the point , find the value of k.
8,3P
1991 Extension 1 HSC Q1c)
4,6
• Draw the endpoints, ratio and cross the same as usual
4,6 4,0
1:k
10613
k
k
1:3ratioin theexternally divides ABP
4,0
• Create the fraction for the either the x value or the y value (it does not matter which one) and equate it with the known value
633 k
393
kk
Exercise 5A;1ad, 2ad,
3 i, iii in all, 4ace,5 i, ii ace, 6bd,
8, 9, 11, 13b, 16,17, 20, 21, 23, 24
Recommended