If the points A(x, 2), B(– 3, – 4) and C(7, – 5) are collinear, then the value of x is :

Engineering

Mathematics

Introduction to Determinants

Question

– 63

– 60

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Given points are A(x, 2), B(– 3, – 4), C(7, – 5)

(x₁, y₁) = (x, 2), (x₂, y₂) = ( – 3, – 4) (x₃, y₃) = (7, – 5)

x₁[y₂ – y₃] + x₂[y₃ – y₁] + x₃[y₁ – y₂] = 0

x[( – 4) – (– 5)] + (– 3)[( – 5) – 2] + 7[2 – ( – 4)] = 0

x(– 4 + 5) – 3( – 5 – 2) + 7(2 + 4) = 0

x(1) – 3( – 7) + 7(6) = 0

x + 21 + 42 = 0

x + 63 = 0

x = – 63

∴ The value of x is – 63.

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