Question

How do you find the distance between the points $\left(3,7\right)$, $\left(-2,-5\right)$?

Answer 1

Find the distance between the two given points:

Distance between the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given as-

$d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Here, points are $\left(3,7\right)$ and $\left(-2,-5\right)$.

$x_1=3,y_1=7,x_2=-2,y_2=-5$.

So, distance is calculated as-

$$\begin{gathered} d=\sqrt{{\left(-2-3\right)}^2+{\left(-5-7\right)}^2} \\ \Rightarrow d=\sqrt{{\left(-5\right)}^2+{\left(-12\right)}^2} \\ \Rightarrow d=\sqrt{25+144} \\ \Rightarrow d=\sqrt{169} \\ \therefore d=13 \end{gathered}$$

Hence, the distance between the points $\left(3,7\right)$ and $\left(-2,-5\right)$ is $13$.