The coordinates of vertices a and b are a(3,4) and b(3,12). if the area of triangle abc is 24 square units, what could be the coordinates of point c?

 Ans: C(9,4)

Rationale: 

We see (3,4) and (3,12) lie on the same line x=3, forming a leg of a triangle. We deduce the length of the side is 8 units. We want a triangle with an area of 24 units. However, recall that the area of a right triangle is simply half the area of the rectangle formed by the two legs. Thus with one leg 8 units and the desired area of our rectangle 48 units, we have 48/8 = 6 units. Thus the other leg of the triangle has a length of 6 units. Adding 6 units to the x-value of the point A, we have C = (9,4).