Question

find the distance d(p₁, p₂) between the points p₁ and p₂. p₁=(3, - 5) p₂=(5,3) 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 $x_1 = 3,y_1=-5,x_2 = 5,y_2 = 3$.

Step2: Substitute values

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

Step3: Calculate squares

$d(P_1,P_2)=\sqrt{4+64}$.

Step4: Simplify

$d(P_1,P_2)=\sqrt{68}=\sqrt{4\times17}=2\sqrt{17}$.

Answer:

$2\sqrt{17}$