Question

find the distance between each pair of points. 9. c(-3, -1), q(-2, 3)

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, $x_1=-3,y_1 = - 1,x_2=-2,y_2 = 3$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-2-(-3)=-2 + 3=1$, $y_2 - y_1=3-(-1)=3 + 1 = 4$.

Step3: Square differences and sum

Square the results from Step 2: $(x_2 - x_1)^2=1^2 = 1$, $(y_2 - y_1)^2=4^2 = 16$. Then sum them: $(x_2 - x_1)^2+(y_2 - y_1)^2=1 + 16=17$.

Step4: Take square - root

$d=\sqrt{17}$.

Answer:

$\sqrt{17}$