A triangle has two of its vertices at 0 , 1 and 2 , 2 in the Cartesian plane. Its third vertex lies on the x -axis. If the area of the triangle is 2 square units, then the sum of the square of the possible values of abscissa of the third vertex is

Question

A triangle has two of its vertices at 0 , 1 and 2 , 2 in the Cartesian plane. Its third vertex lies on the x -axis. If the area of the triangle is 2 square units, then the sum of the square of the possible values of abscissa of the third vertex is, 40, 10, 52, 61

MARKS App · Accepted Answer

Let, the third vertex be a , 0 Area of triangle, Δ = 1 2 0 1 1 2 2 1 a 0 1 = 2 ∴ 0 0 1 2 1 1 a - 1 1 = 4 ⇒ a + 2 = 4 i.e. a = 2 or a = - 6 Hence, the sum of the square of the possible values of abscissa = 40

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