Question

calculate the distance between the points g = (-1, 5) and h = (3, -2) in the coordinate plane. give an exact answer (not a decimal approximation)

Explanation:

Step1: Identify distance formula

$d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$

Step2: Substitute coordinates

Let $(x_1,y_1)=(-1,5)$ and $(x_2,y_2)=(3,-2)$. Then $d=\sqrt{(3 - (-1))^2+((-2)-5)^2}=\sqrt{(4)^2+(-7)^2}=\sqrt{16 + 49}=\sqrt{65}$

Answer:

$\sqrt{65}$