Chapter 13, Problem 1RE

For Exercises 1-2, find the distance between the two points by using the distance formula.

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

To determine

To calculate: The distance between the points $\left(-6,3\right)$ and $\left(0,1\right)$ by using the distance formula.

Answer to Problem 1RE

Solution:

The distance between the points $\left(-6,3\right)$ and $\left(0,1\right)$ is $\underset{\_}{2\sqrt{10}}$.

Explanation of Solution

Given Information:

The points are, $\left(-6,3\right)$ and $\left(0,1\right)$.

Formula used:

Distance formula:

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

Calculation:

The points are $\left(-6,3\right)$ and $\left(0,1\right)$.

Here, $x_1=-6,x_2=0,y_1=3,y_2=1$

To find the distance between the two points use distance formula,

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

Substitute $x_1=-6,x_2=0,y_1=3,y_2=1$ in the above formula.

$\begin{array}{ccc}\hfill d& =& \sqrt{{\left(0-(-6)\right)}^2+{\left(1-3\right)}^2}\hfill \\ \hfill & =& \sqrt{{\left(6\right)}^2+{\left(-2\right)}^2}\hfill \\ \hfill & =& \sqrt{36+4}\hfill \\ \hfill & =& \sqrt{40}\hfill \end{array}$

Further,

$d=2\sqrt{10}$

Thus, the distance between the two points $\left(-6,3\right)$ and $\left(0,1\right)$ is $2\sqrt{10}$.