Coordinate Geometry-10

Find the area of the quadrilateral formed by joining the points A (5, 0), B (3, 4), C (-4, 1) and D (2, -3).

Solution: The are of the quadrilateral ABCD = area of Triangle ABC + area of Triangle ACD

Area of Triangle ABC = 1/2 [5(4 - 1) + 3(1 - 0) - 4(0 - 4)]

= 1/2 (15 + 3 + 16) = 34/2 = 17

Area of Triangle = 1/2 [5(1 + 3) - 4(-3 - 0) + 2(0 - 1)]

= 1/2 (20 + 12 - 2) = 30/2 = 15

Therefore, Area of quadrilateral = ABCD = area of Triangle ABC + area of Triangle ACD = 17 + 15 = 32 square units.