Question

What is the distance between (-5, 7) and (4, -2)

Answer 1

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have

`(-5,\ 7)\to x_1=-5,\ y_1=7\\(4,\ -2)\to x_2=4,\ y_2=-2`

Substitute:

`d=√((4-(-5))^2+(-2-7)^2)=√(9^2+(-9)^2)=√(81+81)=√(81\cdot2)\\\\=√(81)\cdot\sqrt2=\boxed{9\sqrt2}`