Question

find the distance d(p1, p2) between the points p1 and p2. p1 = (-3, 2); p2 = (6, 0) d(p1, p2) = □ (type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall distance formula

The distance formula between two points $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ is $d(P_1,P_2)=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = 2,x_2=6,y_2 = 0$.

Step2: Substitute values

Substitute the values into the formula: $d(P_1,P_2)=\sqrt{(6-(-3))^2+(0 - 2)^2}=\sqrt{(6 + 3)^2+( - 2)^2}=\sqrt{9^2+(-2)^2}=\sqrt{81 + 4}$.

Step3: Simplify

$\sqrt{81+4}=\sqrt{85}$.

Answer:

$\sqrt{85}$