Question

calculate the distance between the points e = (-8, 7) and f = (-3, 3) in the coordinate plane. give an exact answer (not a decimal approximation).

Explanation:

Step1: Recall distance formula

The distance $d$ 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 $(x_1,y_1)=(-8,7)$ and $(x_2,y_2)=(-3,3)$

Step3: Compute differences

$x_2-x_1=-3-(-8)=5$, $y_2-y_1=3-7=-4$

Step4: Square and sum differences

$(5)^2+(-4)^2=25+16=41$

Step5: Take square root

$d=\sqrt{41}$

Answer:

$\sqrt{41}$