How do you find the distance between #P(-5, -4)# and #P(7, 5)#?
Use Pythagoras' Theorem 😃
Imagine that the distance between two points is the hypotenuse of a triangle. We need to find the base and the height of the triangle to get the hypotenuse.
First, find the distance between the x-coordinates. You find the distance between the two x-coordinates along the same y-coordinate. This is found by counting the distance from 0 to another point and adding those together.
-5 to get to 0 takes 5 units.
0 to 7 takes 7 units.
Where the distance ends is (7,-4) because the original coordinate was (-5, -4).
Second, do the same now but for the y-coordinates. From (7,-4) count how many units it takes to get to (7, 5).
From -4 to 0 takes 4 units.
0 to 5 takes 5 units.
4+5 = 9 units.
Now that we have the base and height, we use Pythagoras' Theorem to find the distance:
Hope this helps!