Question

find the distance between (-8, 7) and (8, 2). provide an answer accurate to the nearest hundredth.

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, $(x_1,y_1)=(-8,7)$ and $(x_2,y_2)=(8,2)$.

Step2: Calculate differences

$x_2 - x_1=8-(-8)=16$ and $y_2 - y_1=2 - 7=-5$.

Step3: Square the differences

$(x_2 - x_1)^2=16^2 = 256$ and $(y_2 - y_1)^2=(-5)^2 = 25$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=256 + 25=281$.

Step5: Calculate the square - root

$d=\sqrt{281}\approx16.763$.

Step6: Round to the nearest hundredth

$d\approx16.76$.

Answer:

$16.76$