This is not rocket science guys. You only need to know 4 things to solve what silver is asking:

1. y-y1 = m(x-x1) .... the point-slope form of a line

2. slope m = dy/dx given two points p1 and p2 m = (y2-y1)/(x2-x1)

3. if L1 has a slope of m and is perpendicular to L2 then L2 has a slope of -1/m

4. dist btween two points p1 and p2 is dist = sqrt(dy^2 + dx^2) = sqrt((y2-y1)^2 + (x2-x1)^2)

With those four things you can solve for all the things he asked for.

and I have no idea why he is asking about 2D rotation matrices when his question is about finding the equation of a line given two points and the shortest distance from a point to line, unless this is all just a joke and he is trying to see how much time he can make people waste.

In fact his second question was "what is the distance from p3(-500,400) to line L1?" Well, silver if that is the exact question you were asked then there are an infinite number of answers. PROOF: L1 is infinite and therefore has an infinite number of points, so you can draw an infinite number of lines from p3 to any point on L1 and therefore compute a distance for each line drawn and thus have an infinite number of distances from p3 to the line L1. QED

Note: even if L1 is just the line segment from p1 to p2 it still has an infinite number of points that can be defined along the line and therefore would have an infinite number of lines that could be drawn from a point on L1 to the point p3. So the proof above still holds true. QED