Chapter 9, Problem 1RP

In exercises 1 and 2, find the distance between the points.

$\left(0,-6\right)\text{and}\left(-3,2\right)$

To determine

To calculate: The distance between the points $\left(0,-6\right)$ and $\left(-3,2\right)$.

Answer to Problem 1RP

Solution:

The distance between the points $\left(0,-6\right)$ and $\left(-3,2\right)$ is $\sqrt{73}$ units.

Explanation of Solution

Formula used:

The distance $d$ between two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by,

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

Calculation:

Consider the points $\left(0,-6\right)$ and $\left(-3,2\right)$.

The distance between the two points $\left(0,-6\right)$ and $\left(-3,2\right)$ be $d$.

Then,

Calculate $d$ as follows,

$\begin{array}{c}d=\sqrt{{\left(-3-0\right)}^2+{\left(2-\left(-6\right)\right)}^2}\\ =\sqrt{9+{\left(2+6\right)}^2}\\ =\sqrt{9+64}\\ =\sqrt{73}\end{array}$

Therefore, the distance between the points $\left(0,-6\right)$ and $\left(-3,2\right)$ is $\sqrt{73}$ units.