Question

Prove that the points (2, 3), (-4, -6) and (1, 3/2) do not form a triangle.

Answer 1

we have to prove that, points (2, 3), (-4, -6) and (1, 3/2) do not form a triangle.

concept : if [x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] = 0 , then (x₁, y₁) , (x₂, y₂) and (x₃, y₃) do not form a triangle.

so, [2(-6 - 3/2) + (-4)(3/2 - 3) + 1(3 - (-6)) ]

= 2(-15/2) + (-4)(-3/2) + 9

= -15 + 6 + 9

= -15 + 15

= 0

hence it is clear that points (2, 3), (-4, -6) and (1, 3/2) do not form a triangle.

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