Question

find the distance between the pair of points. e(10, - 2), f(-2,7)
d = (simplify your answer. type an exact answer, using radicals as needed.)

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 $(x_1,y_1)=(10,-2)$ and $(x_2,y_2)=(-2,7)$. Then $x_2 - x_1=-2 - 10=-12$ and $y_2 - y_1=7-(-2)=9$.

Step3: Calculate the squares

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

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=144 + 81=225$.

Step5: Take the square - root

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

Answer:

$15$