Q. 10 - Geometry

Question

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

 (-2, -2) and (5, 7)

Step-by-Step Solution

Answer

The distance is $\sqrt{130}$.

Step-1 – Given

The given points are (-2, -2) and (5, 7).

Step-2 – To determine

We have to find the distance between the two points.

Step-3 – Calculation

$Let\left(x_1,y_1\right)\text{ = }\left(-2,-2\right)\text{ and }\left(x_2,y_2\right)\text{ = }\left(5,7\right)$.

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:

$\begin{array}{l}d=\sqrt{{\left(5-\left(-2\right)\right)}^2+{\left(7-\left(-2\right)\right)}^2}\\ d=\sqrt{{\left(5+2\right)}^2+{\left(7+2\right)}^2}\\ d=\sqrt{{\left(7\right)}^2+{\left(9\right)}^2}\\ d=\sqrt{49+81}\\ d=\sqrt{130}\end{array}$

Hence, the required distance is $\sqrt{130}$.