Question

Find the distance between the origin and the point $(-8,15)$.

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 $(-8,15)$ and therefore,

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}=\sqrt{{(-8-0)}^2+{(15-0)}^2}=\sqrt{{(-8)}^2+{15}^2}=\sqrt{64+225}=\sqrt{289}=\sqrt{{17}^2}=17$

Hence, the distance is $17$ units.