I want to find the distance between a point and an x or y axis, but at a certain angle. Hopefully the diagram below will be able to better explain what I am looking for.

I am trying to find the distance of the red and blue lines, the distance between point $p$ and the x-axis, and point $p$ and y-axis respectfully.

The lines originate from an arbitrary point $p$ and are angled by an arbitrary angle $\theta$ and $\theta+90^\circ$

enter image description here

  • 1
    $\begingroup$ do you know trigonometry? $\endgroup$ – dcolazin May 31 '19 at 20:02
  • $\begingroup$ Can we assume that x, y of P are given. How P is given? $\endgroup$ – Moti Jun 1 '19 at 1:27
  • $\begingroup$ You need to use Patagonian equations $\endgroup$ – Moti Jun 1 '19 at 1:29
  • $\begingroup$ You need to be sure of sign of coordinate and sign of angle (conventionally CCW is taken positive) . Inclined length by trig is more in magnitude. $L_x = |x|/\cos \theta ,\, L_y = |y|/\cos \theta $ $\endgroup$ – Narasimham Jun 1 '19 at 18:14

This is not difficult, the distance to axis $y$ will be $\large{\frac{|x|}{\sin \theta}}$, the distance to axis $x$ will be $\large{\frac{|y|}{\sin \theta}}$. Just draw lines parallel to axes and consider right triangles that will be formed by constructed lines, axes and your red and blue lines.


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