Chapter 13.1, Problem 10WE

To determine

To find the distance between the two points

Answer to Problem 10WE

The values of d are $\sqrt{130}$

Explanation of Solution

Given information:

The given points is

  $\left(-2,-2\right)\text{ and }\left(5,7\right)$

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, $\left(x_1,y_1\right)\text{ be }\left(-2,-2\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(5,7\right)$

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 $x_1=-2,x_2=5,y_1=-2\text{ and }{y}_2=7$ on the above equation

  $\begin{array}{l}d=\sqrt{{\left(5-\left(-2\right)\right)}^2+{\left(7-\left(-2\right)\right)}^2}\\ d=\sqrt{{\left(5+2\right)}^2+{\left(7+2\right)}^2}\\ d=\sqrt{{\left(7\right)}^2+{\left(9\right)}^2}\\ d=\sqrt{49+81}\\ d=\sqrt{130}\end{array}$

Hence,

The values of d are $\sqrt{130}$