189. An altitude of a triangle is a segment that joins one ofthe three vertices to a point on the line that contains theopposite 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 sideAB. What is the area of ABC? (b) Find an equation for the line thatcontains the altitude from A to side BC. (c) Find an equation forthe line BC. (d) Find coordinates for the point F where thealtitude from A meets side BC. It is customary to call F the footof the altitude from A. (e) Find the length of the altitude from Ato side BC. (f) As a check on your work, calculate BC and multiplyit by your answer to part (e). You should be able to predict theresult. (g) It is possible to deduce the length of the altitudefrom B to side AC from what you have already calculated. Showhow.
