Q. 8WE - Geometry

Question

Use the distance formula to find the distance between the two points.

1.  (12, -1) and (0, -6)

Step-by-Step Solution

Answer

The distance is 13.

Step-1 – Given

The given points are (12, -1) and (0, -6). 

Step-2 – To determine

We have to find the distance between the two points using the distance formula.

Step-3 – Calculation

$Let \left(x_1,y_1\right)\text{ = }\left(12,-1\right)\text{ and }\left(x_2,y_2\right)\text{ = }\left(0,-6\right)\text{.}$

Using the distance formula $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\left[d=\text{distance}\right]$we get:

$\begin{array}{l}d=\sqrt{{\left(0-12\right)}^2+{\left(-6-\left(-1\right)\right)}^2}\\ d=\sqrt{{\left(0-12\right)}^2+{\left(-6+1\right)}^2}\\ d=\sqrt{{\left(-12\right)}^2+{\left(-5\right)}^2}\\ d=\sqrt{144+25}\\ d=\sqrt{169}\\ d=13\end{array}$

Hence, the required distance is 13.