Chapter 13.1, Problem 3WE

To determine

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

Answer to Problem 3WE

The value of AB are 4

Explanation of Solution

Given information:

The given point is

  $\left(3,-4\right)\text{ and }\left(-1,-4\right)$

Calculation:

The distance between the two points can be calculated as

Let, coordinate of $A\left(x_1,y_1\right)\text{ be }A\left(3,-4\right)\text{ and }B\left(x_2,y_2\right)\text{ be }B\left(-1,-4\right)$

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

The coordinates of T are $\left(x_2,y_1\right)=\left(-1,-4\right)$

Then,

  $\begin{array}{l}AT=\left(x_1-x_2\right)\\ AT=\left(3-\left(-1\right)\right)\\ AT=\left(3+1\right)\\ AT=4\end{array}$

And

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

Therefore,

  $\begin{array}{l}{\left(AB\right)}^2={\left(AT\right)}^2+{\left(BT\right)}^2\\ {\left(AB\right)}^2={\left(4\right)}^2+{\left(0\right)}^2\\ {\left(AB\right)}^2=16+0\\ {\left(AB\right)}^2=16\\ AB=4\end{array}$

Hence,

The value of AB are 4