Question

find the distance between the points (-7, -9) and (-6, -5). 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, $x_1=-7,y_1 = - 9,x_2=-6,y_2=-5$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-6-(-7)=-6 + 7=1$ and $y_2 - y_1=-5-(-9)=-5 + 9 = 4$.

Step3: Substitute into formula

Substitute into the distance formula: $d=\sqrt{(1)^2+(4)^2}=\sqrt{1 + 16}=\sqrt{17}$.

Answer:

$\sqrt{17}$