How to find coordinates of reflected point? How can I find the coordinates of a point reflected over a line that may not necessarily be any of the axis? 
Example Question: 

If P is a reflection (image) of point (3, -3) in the line $2y = x+1$, find the coordinates of Point P. 

I know the answer is $(-1,5)$ by drawing a graph but other than that, I cannot provide any prior workings because I don't know how to start...

Find line perpendicular to $ 2y=x+1$ which passes through $(3, -3)$

$$2x+y=3$$

Find intersection point of those two lines ( Foot of perpendicular )

$$(1,1)$$

Use Mid-Point Formula (special case of Section formula) to get required point (Foot of perpendicular is mid-point of reflection and original point)

$$(-1,5)$$

