Question

find the distance d(p1, p2) between the points p1 and p2. p1=(5, - 5) p2=(3,1) d(p1, p2)= (simplify your answer. type an exact answer, using radicals as needed.)

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 $x_1 = 5,y_1=- 5,x_2 = 3,y_2 = 1$.

Step2: Substitute values

$d=\sqrt{(3 - 5)^2+(1-(-5))^2}=\sqrt{(-2)^2+(1 + 5)^2}$.

Step3: Calculate squares

$d=\sqrt{4+36}$.

Step4: Simplify

$d=\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}$.

Answer:

$2\sqrt{10}$