How can I draw a line which is perpendicular to a line at a specific point?

Question

I have a line. It can be counter clock-wise or clock wise on $x$-axis. But I want to draw a perpendicular line to it. How can I do that? In the uploaded picture, I explain everything.

Answer 1

Get the equation of your line,

And use,

Eqn of line $$ax+by+c=0$$ Eqn of line perpendicular $$bx-ay+d=0$$

Find $\color{red}{d}$ for the perpendicular line passing through the point of intersection

by putting in x-coordinates and y-coordinates of point of intersection.

Put x=147 in perpendicular line's equation and get y-coordinate of intersection.

Answer 2

Let your red start point be $(a^*, b^*)$ your line has the form. $y = \frac{-1}{m}x + c$ where $m = \tan(7.6^\circ)$. You can figure out c since it passes through $(a^*, b^*)$. Now, set x=0 to see that it meets the y-axis at $(c,0)$