Question

Find the distance between the points named. Use any method you choose.

1. (-2, 3) and (3, -2)

Short answer

The distance is$\sqrt{50}.$

Step-by-step solution

Step-1 – Given

The given points are (-2, 3) and (3, -2).

Step-2 – To determine

We have to find the distance between the two points.

Step-3 – Calculation 

$Let\left(x_1,y_1\right)\text{=}\left(-2,3\right)\text{and}\left(x_2,y_2\right)\text{=}\left(3,-2\right)$

Using the distance formula $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\left[d=\text{distance}\right]$we get:

$\begin{array}{l}d=\sqrt{{\left(3-\left(-2\right)\right)}^2+{\left(-2-3\right)}^2}\\ d=\sqrt{{\left(3+2\right)}^2+{\left(-2-3\right)}^2}\\ d=\sqrt{{\left(5\right)}^2+{\left(-5\right)}^2}\\ d=\sqrt{25+25}\\ d=\sqrt{50}\end{array}$

Hence, the required distance is $\sqrt{50}$.