Q. 2 C5.0( 1 Vote )

Vertices of the triangles taken in order and their areas are given below. In each of the following find the value of a.

Vertices: (a, –3), (3, a), (–1,5)

Area (in sq. units): 12

Answer :

Vertices of triangle A (a, –3), B (3, a) and C (–1, 5)


Area of triangle = 12 sq. units


Area of triangle =


x1 = a, x2 = 3 and x3 = –1


y1 = –3, y2 = a and y3 = 5





12 × 2 = a2 – 4a + 27


24 = a2 – 4a + 27


a2 – 4a + 27 – 24 = 0


a2 – 4a + 3


a2 – 3a – a + 3 = 0


a (a 3) (a 3) = 0


(a 3) (a 1) = 0


a – 3 = 0 or a – 1 = 0


a = 3 or a = 1


Therefore, the required vertices are (3, –3) or (1, –3)


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