Question

find the distance between the points (2, 5) and (-7, -7). 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, $x_1 = 2,y_1 = 5,x_2=-7,y_2 = - 7$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-7 - 2=-9$ and $y_2 - y_1=-7 - 5=-12$.

Step3: Square the differences

$(x_2 - x_1)^2=(-9)^2 = 81$ and $(y_2 - y_1)^2=(-12)^2 = 144$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 144=225$.

Step5: Take the square - root

$d=\sqrt{225}=15$.

Answer:

15