Question

calculate the distance between the points l = (-9, 3) and q = (-1, 9) in the coordinate plane. give an exact answer (not a decimal approximation). distance:

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(-9,3)$ and $(x_2,y_2)=(-1,9)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-1-(-9)=-1 + 9=8$, $y_2 - y_1=9 - 3 = 6$.

Step3: Square differences and sum

Square the differences: $(x_2 - x_1)^2=8^2 = 64$, $(y_2 - y_1)^2=6^2=36$. Then sum them: $(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 36=100$.

Step4: Take square - root

$d=\sqrt{100}=10$.

Answer:

$10$