Question

find the distance d(p1, p2) between the points p1 and p2. p1=(4, - 4); p2=(3,2) 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 $P_1(x_1,y_1)$ 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 $x_1 = 4,y_1=-4,x_2 = 3,y_2 = 2$.

Step2: Substitute values

$d(P_1,P_2)=\sqrt{(3 - 4)^2+(2-(-4))^2}=\sqrt{(-1)^2+(2 + 4)^2}$.

Step3: Calculate squares

$=\sqrt{1+36}$.

Step4: Simplify

$=\sqrt{37}$.

Answer:

$\sqrt{37}$