Geometry (C10)

If the area of triangle with vertices (x, 3), (4, 4) and (3, 5) is 4 square units, find x.

Answer

Ar (∆ABC) = 4

⇒ ½[x(4 – 5) + 4(5 – 3) + 3(3 – 4)] = 4

⇒ (–x + 5) = 8

⇒ x = –3