Question

Calculate the distance between the points G=(-9, 8) and H=(-2, 2) in the coordinate plane.

Answer 1

Answer:

$\sqrt{153}$

Step-by-step explanation:

Using Pythagoras in 3D.

$a^2+b^2=c^2$ (The distance between two points in a direction)

For the x-plane.

$(-9)^2+(-2)^2=c^2\\85=c^2\\c=\sqrt{85}$

For the y-plane.

$8^2+2^2=c^2\\68=c^2\\c=\sqrt{68}$

Finding the shortest distance between those two points.

$\sqrt{68}^2+\sqrt{85}^2=c^2\\68+85=c^2\\153=c^2\\c=\sqrt{153}$