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2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
Let's find the distance between two points.
So the distance from (-6,4) to (1,4) is 7.
If the points are located horizontally from each other, the y coordinates will be the same. You can look to see how far apart the x coordinates are.
(1,4)(-6,4)
7 units apart
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
What coordinate will be the same if the points are located vertically from each other?
So the distance from (-6,4) to (-6,-3) is 7.
If the points are located vertically from each other, the x coordinates will be the same. You can look to see how far apart the y coordinates are.
(-6,-3)
(-6,4)
7 units apart
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
But what are we going to do if the points are not located either horizontally or vertically to find the distance between them?
Let's add some lines and make a right triangle.
This triangle measures 4 units by 3 units on the sides. If we find the hypotenuse, we'll have the distance from (0,0) to (4,3)
Let's start by finding the distance from (0,0) to (4,3)
?
4
3
The Pythagorean Theorem will help us find the hypotenuse
222 cba 222 34 c
2916 c
5c
5
So the distance between (0,0) and (4,3) is 5 units.
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 0 4 6 8
7
123456
8
-2-3-4-5-6-7
Now let's generalize this method to come up with a formula so we don't have to make a graph and triangle every time.
Let's add some lines and make a right triangle.
Solving for c gives us:
Let's start by finding the distance from (x1,y1) to (x2,y2) ?
x2 - x1
y2 – y1
Again the Pythagorean Theorem will help us find the hypotenuse
222 cba (x2,y2)
(x1,y1)
22
122
12 cyyxx
212
212 yyxxc
This is called the distance formula
212
212 yyxxc
Let's use it to find the distance between (3, -5) and (-1,4)
(x1,y1) (x2,y2)
3-1 -54
2294 c 8116 8.997
CAUTION!
You must do the brackets first then powers (square the numbers) and then add together BEFORE you can square root
Don't forget the order of operations!
means approximately equal to
found with a calculator
Plug these values in the distance formula
