Q. 5 - Geometry

Question

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

1.  (-6, -2) and (-7, -5)

Step-by-Step Solution

Answer

The distance is  $\sqrt{10}$.

Step-1 – Given

The given points are (-6, -2) and (-7, -5). 

Step-2 – To determine

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

Step-3 – Calculation

Let $\left(x_1,y_1\right)\text{ = }\left(-6,-2\right)\text{ and }\left(x_2,y_2\right)\text{ = }\left(-7,-5\right)$.

Using the distance formula

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

$\begin{array}{l}d=\sqrt{{\left(-7-\left(-6\right)\right)}^2+{\left(-5-\left(-2\right)\right)}^2}\\ d=\sqrt{{\left(-7+6\right)}^2+{\left(-5+2\right)}^2}\\ d=\sqrt{{\left(-1\right)}^2+{\left(-3\right)}^2}\\ d=\sqrt{1+9}\\ d=\sqrt{10}\end{array}$

Hence, the required distance is $\sqrt{10}$.