Question

calculate the distance between the points l = (-1, 5) and p = (2, -2) in the coordinate plane. give an exact answer (not a decimal approximation). distance: \boxed{}

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, \(L = (-1, 5)\) so \(x_1=-1,y_1 = 5\) and \(P=(2,-2)\) so \(x_2 = 2,y_2=-2\).

Step2: Substitute values into formula

Calculate \(x_2 - x_1=2-(-1)=3\) and \(y_2 - y_1=-2 - 5=-7\). Then, \(d=\sqrt{(3)^2+(-7)^2}=\sqrt{9 + 49}=\sqrt{58}\).

Answer:

\(\sqrt{58}\)