Question

find the distance d(p1, p2) between the points p1 and p2. p1=(1, -2) p2=(5,2) 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 $x_1 = 1,y_1=-2,x_2 = 5,y_2 = 2$.

Step2: Substitute values

$d=\sqrt{(5 - 1)^2+(2-(-2))^2}=\sqrt{(4)^2+(4)^2}$.

Step3: Calculate squares

$d=\sqrt{16 + 16}=\sqrt{32}$.

Step4: Simplify radical

$d=\sqrt{16\times2}=4\sqrt{2}$.

Answer:

$4\sqrt{2}$