Question

If the area of triangle ABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 square units, then prove that x + y = 15 ?

Answer 1

It is known that the area of a triangle whose vertices are (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by the numerical value of the expression `1/2[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]`

The vertices of ΔABC are given as A (x, y), B (1, 2) and C (2, 1) is given by

Area of ΔABC

`1/2[x(2-1)+1xx(1-y)+2(y-2)]`

`1/2[x+1-y+2y-4]`

`1/2[x+y-3]`

The area of ΔABC is given as 6.

`rArr 1/2[x+y-3]=6rArrx+y-3=12`

`thereforex+y=15`