Question

In the following exercise, find the distance between the points. Round to the nearest tenth if needed:

$\left(8,2\right)$and$\left(-7,-3\right)$

Short answer

15.8

Step-by-step solution

Step 1. Given information.

The coordinate of the two points are$\left(8,2\right)$and$\left(-7,-3\right)$.

Step 2. Finding the distance between the two points. 

The distance between the points $\left(x_1,y_1\right)$and $\left(x_2,y_2\right)$can be expressed as

$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Substituting the values of the given points, the distance between the points $\left(8,2\right)$and $\left(-7,-3\right)$will be

$$\begin{gathered} d=\sqrt{{\left(8-\left(-7\right)\right)}^2+{\left(2-\left(-3\right)\right)}^2} \\ d=\sqrt{{15}^2+5^2} \\ d=\sqrt{250} \\ d=15.811 \end{gathered}$$

Rounding to the nearest tenth, the distance between the two points will be$d=15.8$