Question

Find the distances between the following pairs of points.
$(4,-7)$ and $(-1,5)$.

Answer 1

Distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$

Let $P(4,-7)$ and $Q(-1,5)$

Then, distance between $P$ and $Q$ is

$PQ=\sqrt{{(-1-4)}^2+{(5-(-7\left)\right)}^2}PQ=\sqrt{{(-5)}^2+{\left(12\right)}^2}PQ=\sqrt{25+144}PQ=\sqrt{169}PQ=13$