Question

What is the distance between points (3,8) and (-9,-8)

5
10
15
20

what is the distance between points (2,6) and (5,2)
3
4
5

what is the distance between points (21,16) and (9,11)
13
12
22
24

Answer 1

It is better to graph these points, to easily understand that the distance of the two points form the hypotenuse of the right triangle. We need to use the Pythagorean theorem to solve for the distance of the two points.

a² + b² = c² ; a = x value ; b = y value

1) (3,8) and (-9,-8)
a = 3 - (-9) = 3 + 9 = 12 ⇒ 12² = 144
b = 8 - (-8) = 8 + 8 = 16 ⇒ 16² = 256 ⇒⇒ 144 + 256 = 400 ; c = √400 = 20

2) (2,6) and (5,2)
a = 2 - 5 = 3 ⇒ 3² = 9
b = 6 - 2 = 4 ⇒ 4² = 16 ⇒⇒ 9 + 16 = 25 ; c = √25 = 5

3) (21,16) and (9,11)
a = 21 - 9 = 12 ⇒ 12² = 144
b = 16 - 11 = 5 ⇒ 5² = 25 ⇒⇒ 144 + 25 = 169 ; c = √169 = 13