Chapter 13.1, Problem 1WE

To determine

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

Answer to Problem 1WE

The value of AB are 7

Explanation of Solution

Given information:

The given point is

  $\left(-2,-3\right)\text{ and }\left(-2,4\right)$

Calculation:

The distance between the two points can be calculated as

Let, coordinate of $A\left(x_1,y_1\right)\text{ be }A\left(-2,-3\right)\text{ and }B\left(x_2,y_2\right)\text{ be }B\left(-2,4\right)$

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

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

Then,

  $\begin{array}{l}AT=\left(x_1-x_2\right)\\ AT=\left(-2-\left(-2\right)\right)\\ AT=\left(-2+2\right)\\ AT=0\end{array}$

And

  $\begin{array}{l}BT=\left(y_1-y_2\right)\\ BT=\left(-3-4\right)\\ BT=\left(-7\right)\\ BT=-7\end{array}$

Since, BT represents the distance, BT cannot be negative

Therefore,

  $BT=7$

  $\begin{array}{l}{\left(AB\right)}^2={\left(AT\right)}^2+{\left(BT\right)}^2\\ {\left(AB\right)}^2={\left(0\right)}^2+{\left(7\right)}^2\\ {\left(AB\right)}^2=0+49\\ {\left(AB\right)}^2=49\\ AB=7\end{array}$

Hence,

The value of AB are 7