Question

Find the value of ‘a’ for which the following points A(a, 3), B(2,1) and C(5, a) are collinear.
Hence, find the equation of the line.

Answer 1

Answer:

a²-4a-4=0

Step-by-step explanation:

As we know in Geometry

Area of Triangle in Geometry= (1/2) [x₁ (y₂ – y₃ ) + x₂ (y₃ – y₁ ) + x₃(y₁– y₂)]

If the points are collinear then Area =0

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

=>[a (1 – a) + 2 (a – 3 ) + 5(3– 1)]=0

=>2a-a²+2a-6+10=0

=>a²-4a-4=0

equation of the line