Given a line segment from point $A$ to point $B$, how do you find a point $A_2 $ that is perpendicular to the point $A$ at a distance $d$ from $A$? Points $A, B$ and distance $d$ are given.
I cant seem to figure out the correct way to solve this problem and my linear algebra / geometry are a bit rusty. It seems as though using Orthogonal Projection may work since I have the distance but I cant figure out the location of the point. Any ideas?
Take a look at the following Diagram for clarification.
Best Answer
I would use the angles, get the slope of the line as follows: $$ \theta = \arctan\frac{y_B-y_A}{x_B-x_A} $$ Then the coordinates of $A_2$ would be $$ x_{A_2} = x_A+d \cos(90+\theta) \\ y_{A_2} = y_A+d \sin(90+\theta) $$