Question

find the distance between the points (-1, -7) and (4, 0). write your answer as a whole number or a fully simplified radical expression. do not round. units

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, $x_1=-1,y_1 = - 7,x_2 = 4,y_2=0$.

Step2: Substitute values

$d=\sqrt{(4-(-1))^2+(0 - (-7))^2}=\sqrt{(4 + 1)^2+(0 + 7)^2}=\sqrt{5^2+7^2}$.

Step3: Calculate squares

$d=\sqrt{25 + 49}=\sqrt{74}$.

Answer:

$\sqrt{74}$