Question

find the distance between the points (-9, -3) and (2, 1). 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: Substitute the values

Let $(x_1,y_1)=(-9,-3)$ and $(x_2,y_2)=(2,1)$. Then $x_2 - x_1=2-(-9)=11$ and $y_2 - y_1=1 - (-3)=4$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=11^2 = 121$ and $(y_2 - y_1)^2=4^2 = 16$. The sum is $121 + 16=137$.

Step4: Find the distance

$d=\sqrt{137}$.

Answer:

$\sqrt{137}$