Question

Find the distance between the origin and the point $(5,12)$.

Answer 1

We know that the distance between the two points $(x_1,y_1)$ and $(x_2,y_2)$ is

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

Since, the origin has the coordinates $(0,0)$, thus

The given points are $(0,0)$ and $(5,12)$ and therefore,

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{{(5-0)}^2+{(12-0)}^2}=\sqrt{5^2+{12}^2}=\sqrt{25+144}=\sqrt{169}=\sqrt{{13}^2}=13$

Hence, the distance is $13$ units.