Question

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

1. (3, 3) and (-2, 3)

Short answer

The distance is 5.

Step-by-step solution

Step-1 – Given

The given points are (3, 3) and (-2, 3).

Step-2 – To determine

We have to find the distance between the two points without using distance formula.

Step-3 – Calculation 

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

Let T be the point where the horizontal line through A and vertical line through B meets.

So, the coordinate of Tis$\left(x_2,y_1\right)=\left(-2,3\right)$

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

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

Using the Pythagorean theorem, we get:

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

Hence, the required distance is 5.