Chapter 9, Problem 1RE

To determine

The distance between two points by using distance formula

Answer to Problem 1RE

Solution:

The distance between the points $\left(-6,3\right)\text{and}\left(0,1\right)$ is given by

$2\sqrt{10}$

Explanation of Solution

Given:

  $\left(-6,3\right)\text{and}\left(0,1\right)$

Formula Used:

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

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

Calculation:

We have been given the points $\left(-6,3\right)\text{and}\left(0,1\right)$. Thus, we have

  $x_1=-6,y_1=3,x_2=0,y_2=1$

Plugging these values in the distance formula, we get

  $\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ =\sqrt{{\left(0+6\right)}^2+{\left(1-3\right)}^2}\\ =\sqrt{{\left(6\right)}^2+{\left(-2\right)}^2}\\ =\sqrt{36+4}\\ =\sqrt{40}\\ =2\sqrt{10}\end{array}$

Therefore, the distance between the points $\left(-6,3\right)\text{and}\left(0,1\right)$ is given by

$2\sqrt{10}$

Conclusion:

Using the distance formula, the distance between the points $\left(-6,3\right)\text{and}\left(0,1\right)$ is given by

$2\sqrt{10}$