Calculating Coords of a point Perpendicular to a Line, Calculating Coords of Third Point in Angle Given Two Points and Angle

Answer 1

Easy if you understand vectors. Learn about how 2D vectors work and you'll have it. Is that the course you're taking?

1. Take the unit vector from e to A, knowing that a unit vector has length 1. Assume l1 = xi + yj. The perpendicular vector has components that are the reverse of l1 with one sign changed. In this case, l2 = -yi + xj.
2. Take the vector l2 that you got from the first problem and transform it as follows:

cx = -cos(t)y - sin(t)x cy = +sin(t)y + cos(t)x

where t is the rotation angle in radians.

I'll leave the third one for you. Read about 2D vectors and transformations.