Chapter 13.1, Problem 12WE

To determine

To find the distance between the two points

Answer to Problem 12WE

The values of d are $4$

Explanation of Solution

Given information:

The given points is

  $\left(-4,-1\right)\text{ and }\left(-4,3\right)$

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, $\left(x_1,y_1\right)\text{ be }\left(-4,-1\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(-4,3\right)$

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 $x_1=-4,x_2=-4,y_1=-1\text{ and }{y}_2=3$ on the above equation

  $\begin{array}{l}d=\sqrt{{\left(-4-\left(-4\right)\right)}^2+{\left(3-\left(-1\right)\right)}^2}\\ d=\sqrt{{\left(-4+4\right)}^2+{\left(3+1\right)}^2}\\ d=\sqrt{{\left(0\right)}^2+{\left(4\right)}^2}\\ d=\sqrt{0+16}\\ d=\sqrt{16}\\ d=4\end{array}$

Hence,

The values of d are $4$