Question

lesson 4 homework
use the distance formula, given two points
question
find the distance between the points (-6, -7) and (-2, -1).
give an exact answer in simplest radical form. do not round.
provide your answer below.

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 point values

Let $(x_1,y_1)=(-6,-7)$ and $(x_2,y_2)=(-2,-1)$. Then $d=\sqrt{(-2-(-6))^2+(-1 - (-7))^2}=\sqrt{(-2 + 6)^2+(-1+7)^2}=\sqrt{4^2+6^2}$.

Step3: Calculate squares and sum

$\sqrt{4^2+6^2}=\sqrt{16 + 36}=\sqrt{52}$.

Step4: Simplify radical

$\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}$.

Answer:

$2\sqrt{13}$