Question

find the distance between the points (-3, -7) and (4, -2). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify distance formula

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

Step2: Assign values

Let $(x_1,y_1)=(-3,-7)$ and $(x_2,y_2)=(4,-2)$. Then $x_2 - x_1=4-(-3)=7$ and $y_2 - y_1=-2-(-7)=5$.

Step3: Calculate distance

$d=\sqrt{(7)^2+(5)^2}=\sqrt{49 + 25}=\sqrt{74}$.

Answer:

$\sqrt{74}$