Question

find the distance between the pair of points. e(9, - 3), f(- 3,6)
d = □ (simplify your answer. type an exact answer, using radicals as

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(9,-3)$ and $(x_2,y_2)=(-3,6)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-3 - 9=-12$ and $y_2 - y_1=6-(-3)=9$.

Step3: Square the differences

$(x_2 - x_1)^2=(-12)^2 = 144$ and $(y_2 - y_1)^2=9^2 = 81$.

Step4: Sum and square - root

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{144 + 81}=\sqrt{225}=15$.

Answer:

$15$