How can you find the distance between the center and edges of a rectangle - a line from centre to a edge at an angle $\theta$?

Question

I have a case where I know the coordinates $(x,y)$ of the center of the rectangle and its edges where the line is dropped anywhere on the edges $a(x_1,y_1),b(x_2,y_1),c(x_1,y_2),d(x_2,y_2)$.

Say I start drawing a line from center towards any edge of the rectangle and rotate it by a arbitrary angle $ \theta$. I need to know that line vector i.e distance from center to the point on the edge or corner vertex which is connected by the line. Any takers?

Answer 1

This is not an answer to your question, but I just think it helps to visualize the situation, I need to be sure that this is the situation you describe:

To calculate the distance from say $(x,y)$ to $d$, you will need to use the distance formula: $$\text{distance}=\sqrt{(x-x_2)^2 + (y-y_2)^2}$$