Question

find the distance between the pair of points. (-2,1) and (1,-2) the distance, d, is (type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-2,1)\) and \((x_2,y_2)=(1,-2)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values:
\(d=\sqrt{(1-(-2))^2+(-2 - 1)^2}\)
\(=\sqrt{(1 + 2)^2+(-3)^2}\)
\(=\sqrt{3^2+(-3)^2}\)
\(=\sqrt{9 + 9}\)
\(=\sqrt{18}\)
\(=\sqrt{9\times2}\)
\(=3\sqrt{2}\)

Answer:

\(3\sqrt{2}\)