Question

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

Give an exact answer (not a decimal approximation).
10+
8
Distance: 0
+
-10-8
-6
-4
- 2
2
6
8
10
-S
-10

Answer 1

`√(153)`

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=√(85)`

For the y-plane.

`8^2+2^2=c^2\\68=c^2\\c=√(68)`

Finding the shortest distance between those two points.

`√(68)^2+√(85)^2=c^2\\68+85=c^2\\153=c^2\\c=√(153)`