# Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear - Mathematics

Sum

Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear

#### Solution

Let ∆ be the area of the triangle formed by the points (a, b + c), (b, c + a) and (c, a + b).

We have,

∴ ∆ = \frac { 1 }{ 2 } |{a (c + a) + b (a + b) + c (b + c)} – {b (b+ c) + c (c + a) + a (a + b)}|

⇒ ∆ = \frac { 1 }{ 2 } |(ac + a^2 + ab + b^2 + bc + c^2 ) – (b^2 + bc + c^2 + ca + a^2 + ab)|

⇒ ∆ = 0

Hence, the given points are collinear

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