Chapter 13.1, Problem 11WE

To determine

To find the distance between the two points

Answer to Problem 11WE

The values of d are $\sqrt{50}$

Explanation of Solution

Given information:

The given points is

  $\left(-2,3\right)\text{ and }\left(3,-2\right)$

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, $\left(x_1,y_1\right)\text{ be }\left(-2,3\right)\text{ and }\left(x_2,y_2\right)\text{ be }\left(3,-2\right)$

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 $x_1=-2,x_2=3,y_1=3\text{ and }{y}_2=-2$ on the above equation

  $\begin{array}{l}d=\sqrt{{\left(3-\left(-2\right)\right)}^2+{\left(-2-3\right)}^2}\\ d=\sqrt{{\left(3+2\right)}^2+{\left(-2-3\right)}^2}\\ d=\sqrt{{\left(5\right)}^2+{\left(-5\right)}^2}\\ d=\sqrt{25+25}\\ d=\sqrt{50}\end{array}$

Hence,

The values of d are $\sqrt{50}$