Advertisement Remove all ads

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

Advertisement Remove all ads

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

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×