# Lets Play With Coordinates

**Geometry**Level 4

Let \(p_1,p_2\) and \(p_3\) be the lengths perpendicular from the points \((m^2,2 m),(mk,m+k)\) and \(({k}^2,2 k),\) respectively, to the line \[x \cos\alpha +y \sin\alpha +\dfrac{\sin^2\alpha}{\cos\alpha}=0.\]

Then \(p_1, p_2, p_3\) follows a/an \(\text{__________} \).