Question

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

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Identify coordinates

Here $x_1=-5,y_1 = - 1,x_2=-2,y_2 = 2$.

Step3: Substitute values

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

Step4: Simplify

$d=\sqrt{9 + 9}=\sqrt{18}=\sqrt{9\times2}=3\sqrt{2}$.

Answer:

$3\sqrt{2}$