Question

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

Answer 1

3√5

Explanation:

Use the formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

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

`d=√((3-0)^2+(-2-(-8))^2)=√(3^2+6^2)=√(9+36)=√(45)=√((9)(5))\\\\=\sqrt9\cdot\sqrt5=3\sqrt5`

Answer 2

`\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 = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([3-0]^2+[-2-(-8)]^2)\implies d=√((3-0)^2+(-2+8)^2) \\\\\\ d=√(3^2+6^2)\implies d = √(9+36)\implies d=√(45)\implies d\approx 6.71`