Q. 9 - Geometry

Question

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

1.  (5, 4) and (1, -2)

Step-by-Step Solution

Answer

The distance is $\sqrt{52}.$

Step-1 – Given

The given points are (5, 4) and (1, -2). 

Step-2 – To determine

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

Step-3 – Calculation

Let $\left(x_1,y_1\right)\text{ = }\left(5,4\right)\text{ and }\left(x_2,y_2\right)\text{ = }\left(1,-2\right)\text{.}$

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:

$\begin{array}{l}d=\sqrt{{\left(1-5\right)}^2+{\left(-2-4\right)}^2}\\ d=\sqrt{{\left(-4\right)}^2+{\left(-6\right)}^2}\\ d=\sqrt{16+36}\\ d=\sqrt{52}\end{array}$

Hence, the required distance is $\sqrt{52}.$