Chapter 13.1, Problem 8WE

To determine

To find the distance between the two points

Answer to Problem 8WE

The values of d are $13$

Explanation of Solution

Given information:

The given points is

  $\left(12,-1\right)\text{ and }\left(0,-6\right)$

Formula used:

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

Calculation:

The distance between the two points can be calculated as

Let, $\left(x_1,y_1\right)\text{ be }\left(12,-1\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(0,-6\right)$

Use the distance formula between the two points

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

Put the values of $x_1=12,x_2=0,y_1=-1\text{ and }{y}_2=-6$ on the above equation

  $\begin{array}{l}d=\sqrt{{\left(0-12\right)}^2+{\left(-6-\left(-1\right)\right)}^2}\\ d=\sqrt{{\left(0-12\right)}^2+{\left(-6+1\right)}^2}\\ d=\sqrt{{\left(-12\right)}^2+{\left(-5\right)}^2}\\ d=\sqrt{144+25}\\ d=\sqrt{169}\\ d=13\end{array}$

Hence,

The values of d are $13$