Q30 of 49 Page 1

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 or x+y = -9.

Area of a Δ ABC whose vertices are A(x1,y1), B(x2,y2) and C(x3,y3) is given by (1/2)|x1(y2-y3)+ x2(y3-y1)+ x3(y1-y2)| units2


Given-


Area of given Δ ABC = 6


⇒ (1/2)|x(2-1)+1(1-y)+2(y-2)| = 6


⇒ |x+1-y+2y-4)| = 12


⇒ |x+y-3| = 12


⇒ x+y-3 = � 12


Taking +ve sign, we get-


x+y-3 = 12


∴ x+y =15


Taking -ve sign, we get-


x+y-3 = -12


∴ x+y = -9


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