Question

calculate the distance between the points e = (-8, 5) and p = (-2, 8) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Recall distance formula

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

Step2: Assign coordinates

Let $(x_1,y_1)=(-8,5)$ and $(x_2,y_2)=(-2,8)$

Step3: Compute $x$-difference

$x_2-x_1=-2-(-8)=6$

Step4: Compute $y$-difference

$y_2-y_1=8-5=3$

Step5: Substitute into formula

$d=\sqrt{6^2+3^2}=\sqrt{36+9}=\sqrt{45}$

Step6: Simplify radical

$\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$

Answer:

$3\sqrt{5}$