Question

find the distance between the points k = (-7, -3) and l = (-1, 3) in the coordinate plane. give an exact answer (not a decimal approximation).

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: Assign values

Let $(x_1,y_1)=(-7,-3)$ and $(x_2,y_2)=(-1,3)$. Then $x_2 - x_1=-1-(-7)=6$ and $y_2 - y_1=3 - (-3)=6$.

Step3: Substitute into formula

$d=\sqrt{(6)^2+(6)^2}=\sqrt{36 + 36}=\sqrt{72}$.

Step4: Simplify radical

$\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}$.

Answer:

$6\sqrt{2}$