Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

Coordinate Geometry and its Formulas (Distance,Midpoint,Slope)

We will talk about 3 formulas that are used to calculate various pieces of information about pairs of points.

Each formula refers to a set of two points:

(x1, y1) and (x2, y2)

Distance between two points.In general,

x1 x2

y1

y2

A(x1,y1)

B(x2,y2)

Length = x2 – x1

Length = y2 – y1

the formula for Length of AB or Distance between A

and B is

y

x

The Distance Formula

2 22 1 2 1( ) ( )d x x y y

"The Distance Formula" sung to the tune of "On Top of Old Smokey"

When finding the distanceBetween the two points,Subtract the two x'sThe same for the y's.Now square these two numbers,And find out their sum.When you take the square rootThen you are all done!

Or use three blindMice songhttps://www.youtube.com/watch?v=m_iyBtstjzs

Example• Find the distance between A(4,8) and B(1,12)

2 22 1 2 1distance ( ) ( )x x y y

A (4, 8)

B (1, 12)

2 2distance (1 4) (12 8) 2 2distance ( 3) (4)

distance 9 16 25 5

First identify your x 1 , x 2 , y 1 and y 2

x1 y1 x2 y2

More examples

• Find the distance between:– A. (2, 7) and (11, 9)

– B. (-5, 8) and (2, - 4)

2 2(9) (2) 85

2 2(7) ( 12) 193

You try: (2, 2) and (5, -2)

Distance: ________

Midpoint Formula:

2,

21212 yyxx

The Midpoint Formula

1 2 1 2( , ) ,2 2

x x y yx y

"The Midpoint Formula" sung to the tune of "The Itsy Bitsy Spider"

When finding the midpoint of two points on a graph,Add the two x's and cut their sum in half.Add up the y's and divide 'em by a two,Now write 'em as an ordered pairIt’s the middle of the two.

Or use the midpoint cheerhttps://www.youtube.com/watch?v=pNoOYVZPEAQ

Example• Find the midpoint between A(4,8) and B(1,12)

2 1 2 1midpoint ,2 2

x x y y

A (4, 8)

B (1, 12)

1 4 12 8midpoint ,

2 2

midpoint 5,10

2

First identify your x 1 , x 2 , y 1 and y 2

x1 y1 x2 y2

More Examples

• Find the midpoint between:

• A) (2, 7) and (14, 9)

• B) (-5, 8) and (2, - 4)

midpoint = 8,8

-3midpoint = , 2

2

You Try: (2, 2) and (5, -2)

Midpoint: _______

Now you get to practice. Please complete the handout and turn it end at the end of class.

Thanks, have a great weekend.