Question

find the distance between the points (-1, 4) and (8, -8). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify the 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 the values of the points

Let $(x_1,y_1)=(-1,4)$ and $(x_2,y_2)=(8,-8)$. Then $x_2 - x_1=8-(-1)=9$ and $y_2 - y_1=-8 - 4=-12$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=9^2 = 81$ and $(y_2 - y_1)^2=(-12)^2=144$. The sum is $81 + 144=225$.

Step4: Find the square - root

$d=\sqrt{225}=15$.

Answer:

$15$