Question

find the distance d(p₁, p₂) between the given points p₁ and p₂
p₁=(1,2)
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 $x_1 = 1,y_1=2,x_2=-5,y_2 = 3$.

Step2: Substitute values

Substitute the values into the formula: $d(P_1,P_2)=\sqrt{(-5 - 1)^2+(3 - 2)^2}=\sqrt{(-6)^2+1^2}$.

Step3: Calculate squares and sum

First, calculate $(-6)^2=36$ and $1^2 = 1$. Then $(-6)^2+1^2=36 + 1=37$. So $d(P_1,P_2)=\sqrt{37}$.

Answer:

$\sqrt{37}$