An altitude of a triangle is a segment that joins one of the three vertices to a point on the line that contains the opposite side, the intersection being perpendicular. For example, consider the triangle whose vertices are A = (0,0), B= (8,0), and C=(4,12). (a) Find the length of the altitude from C to side AB. What is the area of ABC? (b) Find an equation for the line that contains the altitude from A to side BC. (c) Find an equation for the line BC. (d) Find coordinates for the point F where the altitude from A meets side BC. It is customary to call F the foot of the altitude from A. (e) Find the length of the altitude from A to side BC. (f) As a check on your work, calculate BC and multiply it by your answer to part (e). You should be able to predict the result. (g) It is possible to deduce the length of the altitude from B to side AC from what you have already calculated. Show how.