The lines y = 3x, y = 6, y = 3x - 12 and y = 0 are plotted. The intersection of these lines form quadrilateral ABCD, where A, B is the point on the line y = 6 and C,D is the point on the line y = 0. The point A is (2,6) and the point D is (0,0), and BC is extended such that BC = CQ. AQ intersects DC at P and AC is joined.
Then, area of triangle APC = area of triangle DPQ.
ABCD is a quadrilateral with AB = CD and AB∥CD. A quadrilateral with opposite sides parallel and equal is a parallelogram.
Since, BC = CQ, AD = BC. Thus, AD = CQ. And CB is extended to CQ, then CQ is parallel to AD.
Since, CQ = AD, and CQ∥AD, then ADQC is a parallelogram.
AC is a diagonal of the parallelogram ABCD. DC and AQ are the diagonals of ADQC.
Triangles between the same base and same parallels are equal.
Area of Δ DCQ = Area of Δ QAC (between the parallels AD and CQ).
Area of ΔDCQ - Area of Δ PCQ = Area of Δ QAC- Area of Δ PCQ
⇒ Area of Δ DPQ = Area of ΔAPC