Question

Find the distance between points (0,-8) and (3,-2)

Answer 1

$\bf~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3-0]^2+[-2-(-8)]^2}\implies d=\sqrt{(3-0)^2+(-2+8)^2} \\\\\\ d=\sqrt{3^2+6^2}\implies d = \sqrt{9+36}\implies d=\sqrt{45}\implies d\approx 6.71$

Answer 2

Answer:

3√5

Step-by-step explanation:

Use the formula:

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

Substitute the coordinates of the given points (0, -8) and (3, -2):

$d=\sqrt{(3-0)^2+(-2-(-8))^2}=\sqrt{3^2+6^2}=\sqrt{9+36}=\sqrt{45}=\sqrt{(9)(5)}\\\\=\sqrt9\cdot\sqrt5=3\sqrt5$