Parallelogram ABCD has A(0, 1), B(2, 1) and C(4, 0) as three of its vertices. What is the sum of the coordinates of point D?
Line AB is horizontal. We know that parallelograms have two sets of parallel sides, meaning line CD will also be horizontal, or have a slope of 0.
Next we need to find the slope of line BC, which would be -1/2. That would be parallel to AD.
Point D will be the solution of line CD and AD. The equations for those two lines are:
So we take x=2 and y=0 to get the coordinates (2,0).