Question

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

1. (12, -1) and (0, -6)

Short answer

The distance is 13.

Step-by-step solution

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.