Chapter 13.1, Problem 9WE

To determine

To find the distance between the two points

Answer to Problem 9WE

The values of d are $\sqrt{52}$

Explanation of Solution

Given information:

The given points is

  $\left(5,4\right)\text{ and }\left(1,-2\right)$

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, $\left(x_1,y_1\right)\text{ be }\left(5,4\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(1,-2\right)$

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 $x_1=5,x_2=1,y_1=4\text{ and }{y}_2=-2$ on the above equation

  $\begin{array}{l}d=\sqrt{{\left(1-5\right)}^2+{\left(-2-4\right)}^2}\\ d=\sqrt{{\left(-4\right)}^2+{\left(-6\right)}^2}\\ d=\sqrt{16+36}\\ d=\sqrt{52}\end{array}$

Hence,

The values of d are $\sqrt{52}$