Question

Find the distances between the following pair of points.
$(a,0)$ and $(0,b)$.

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 $P(a,0)$ and $Q(0,b)$

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

$PQ=\sqrt{{(0-a)}^2+{(b-0)}^2}PQ=\sqrt{{(-a)}^2+{\left(b\right)}^2}PQ=\sqrt{a^2+b^2}$