Question

find the distance d(p₁,p₂) between the given points p₁ and p₂.
p₁=(1,0)
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, $x_1 = 1,y_1 = 0,x_2 = 5,y_2 = 3$.

Step2: Substitute values

$d(P_1,P_2)=\sqrt{(5 - 1)^2+(3 - 0)^2}=\sqrt{4^2+3^2}$.

Step3: Calculate squares and sum

$\sqrt{4^2+3^2}=\sqrt{16 + 9}=\sqrt{25}$.

Step4: Simplify square - root

$\sqrt{25}=5$.

Answer:

$5$