Question

find the distance between the points (-1, 2) and (7, 8). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-1,y_1 = 2,x_2=7,y_2 = 8$.

Step2: Substitute values

$d=\sqrt{(7-(-1))^2+(8 - 2)^2}=\sqrt{(7 + 1)^2+(6)^2}=\sqrt{8^2+6^2}$.

Step3: Calculate squares

$\sqrt{64 + 36}=\sqrt{100}$.

Step4: Simplify square - root

$\sqrt{100}=10$.

Answer:

10