Chapter 13.1, Problem 2WE

To determine

To find the distance between the two point without using distance formula

Answer to Problem 2WE

The value of AB are 5

Explanation of Solution

Given information:

The given point is

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

Calculation:

The distance between the two points can be calculated as

Let, coordinate of $A\left(x_1,y_1\right)\text{ be }A\left(3,3\right)\text{ and }B\left(x_2,y_2\right)\text{ be }B\left(-2,3\right)$

Let, T be the coordinate that are draw the horizontal and vertical line of the two given points

The coordinates of T are $\left(x_2,y_1\right)=\left(-2,3\right)$

Then,

  $\begin{array}{l}AT=\left(x_1-x_2\right)\\ AT=\left(3-\left(-2\right)\right)\\ AT=\left(3+2\right)\\ AT=5\end{array}$

And

  $\begin{array}{l}BT=\left(y_1-y_2\right)\\ BT=\left(3-3\right)\\ BT=0\end{array}$

Therefore,

  $\begin{array}{l}{\left(AB\right)}^2={\left(AT\right)}^2+{\left(BT\right)}^2\\ {\left(AB\right)}^2={\left(5\right)}^2+{\left(0\right)}^2\\ {\left(AB\right)}^2=25+0\\ {\left(AB\right)}^2=25\\ AB=5\end{array}$

Hence,

The value of AB are 5