Chapter 13.1, Problem 4WE

To determine

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

Answer to Problem 4WE

The value of AB are 5

Explanation of Solution

Given information:

The given point is

  $\left(0,0\right)\text{ and }\left(3,4\right)$

Calculation:

The distance between the two points can be calculated as

Let, coordinate of $A\left(x_1,y_1\right)\text{ be }A\left(0,0\right)\text{ and }B\left(x_2,y_2\right)\text{ be }B\left(3,4\right)$

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

The coordinates of T are $\left(x_2,y_1\right)=\left(3,0\right)$

Then,

  $\begin{array}{l}AT=\left(x_1-x_2\right)\\ AT=\left(0-3\right)\\ AT=\left(-3\right)\\ AT=-3\end{array}$

Since, AT represents distance, AT cannot be negative

So, $AT=3$

And

  $\begin{array}{l}BT=\left(y_1-y_2\right)\\ BT=\left(0-4\right)\\ BT=\left(-4\right)\\ BT=-4\end{array}$

Since, BT represents distance, BT cannot be negative

So, $BT=4$

Therefore,

  $\begin{array}{l}{\left(AB\right)}^2={\left(AT\right)}^2+{\left(BT\right)}^2\\ {\left(AB\right)}^2={\left(3\right)}^2+{\left(4\right)}^2\\ {\left(AB\right)}^2=9+16\\ {\left(AB\right)}^2=25\\ AB=5\end{array}$

Hence,

The value of AB are 5