Question

Use the distance formula to find the distance between the two points.

1. (3, 2) and (5, -2)

Short answer

The distance is $\sqrt{20}$.

Step-by-step solution

Step-1 – Given

The given points are (3, 2) and (5, -2).

Step-2 – To determine

We have to find the distance between the two points using the distance formula.

Step-3 – Calculation 

$Let\left(x_1,y_1\right)\text{=}\left(3,2\right)\text{and}\left(x_2,y_2\right)\text{=}\left(5,-2\right)$

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:

$\begin{array}{l}d=\sqrt{{\left(5-3\right)}^2+{\left(-2-2\right)}^2}\\ d=\sqrt{{\left(2\right)}^2+{\left(-4\right)}^2}\\ d=\sqrt{4+16}\\ d=\sqrt{20}\end{array}$

Hence, the required distance is $\sqrt{20}$.