Q. 12 - Geometry

Question

Find the distance between the points named. Use any method you choose.

12. (-4, -1) and (-4, 3)

Step-by-Step Solution

Answer

The distance is $\sqrt{50}$.

Step-1 – Given

The given points are (-4, -1) and (-4, 3).

Step-2 – To determine

We have to find the distance between the two points.

Step-3 – Calculation

$Let\left(x_1,y_1\right)\text{ = }\left(-4,-1\right)\text{ and }\left(x_2,y_2\right)\text{ = }\left(-4,3\right)$

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:

$\begin{array}{l}d=\sqrt{{\left(-4-\left(-4\right)\right)}^2+{\left(3-\left(-1\right)\right)}^2}\\ d=\sqrt{{\left(-4+4\right)}^2+{\left(3+1\right)}^2}\\ d=\sqrt{{\left(0\right)}^2+{\left(4\right)}^2}\\ d=\sqrt{0+16}\\ d=\sqrt{16}\\ d=4\end{array}$

Hence, the required distance is 4.