Question

find the distance d(p₁, p₂) between the points p₁ and p₂.
p₁=(3, - 4); p₂=(4,5)
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, $x_1 = 3$, $y_1=-4$, $x_2 = 4$, $y_2 = 5$.

Step2: Substitute values

$d(P_1,P_2)=\sqrt{(4 - 3)^2+(5-(-4))^2}=\sqrt{1^2+(5 + 4)^2}=\sqrt{1+81}$.

Step3: Simplify

$\sqrt{1 + 81}=\sqrt{82}$.

Answer:

$\sqrt{82}$