Question

find the distance $d(p_1,p_2)$ between the points $p_1$ and $p_2$.
$p_1=(4, - 5)$
$p_2=(3,2)$
$d(p_1,p_2)=square$
(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 $x_1 = 4,y_1=- 5,x_2 = 3,y_2 = 2$.

Step2: Substitute values

$d(P_1,P_2)=\sqrt{(3 - 4)^2+(2-(-5))^2}=\sqrt{(-1)^2+(2 + 5)^2}=\sqrt{1 + 49}$.

Step3: Simplify

$d(P_1,P_2)=\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$