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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 ?
Solution
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`
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