Question

find the distance d(p1, p2) between the points p1 and p2. p1=(1, - 1); p2=(4,4) 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 $x_1 = 1,y_1=-1,x_2 = 4,y_2 = 4$.

Step2: Substitute values

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

Step3: Calculate squares and sum

$\sqrt{3^2 + 5^2}=\sqrt{9 + 25}=\sqrt{34}$.

Answer:

$\sqrt{34}$