Question

find the distance d(p1, p2) between the points p1 and p2. p1=(3, - 3); p2=(2,3) 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 $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 3,y_1=-3,x_2 = 2,y_2 = 3$.

Step2: Substitute values

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

Step3: Calculate squares

Calculate the squares: $(-1)^2=1$ and $(3 + 3)^2=6^2 = 36$. So $d=\sqrt{1+36}$.

Step4: Simplify

Simplify the expression: $d=\sqrt{37}$.

Answer:

$\sqrt{37}$