Question

1. what’s the distance between (-8, -6) and (4, 10)?

2. what’s the distance between (5, 14) and (-3, -9)?

Answer 1

Use the formula of a distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$(-8,\ -6),\ (4,\ 10)\\\\d=\sqrt{(4-(-8))^2+(10-(-6))^2}=\sqrt{12^2+16^2}\\\\=\sqrt{144+256}=\sqrt{400}=\boxed{20}\\\\(5,\ 14),\ (-3,\ -9)\\\\d=\sqrt{(-3-5)^2+(-9-14)^2}=\sqrt{(-8)^2+(-23)^2}\\\\=\sqrt{64+529}=\boxed{\sqrt{593}\approx24.35}$