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For what value of x are the points A (_3,12),B (7,6),C (x,9) collinear ?

Posted by Pooja Gupta 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

According to the question, A(-3, 12), B(7, 6) and C(x, 9).
(x₁ = -3, y₁= 12), (x₂ = 7, y₂ = 6) and (x₃ = x, y₃ = 9)
The given points A,B,C are collinear. So, area of triangle is zero.
{tex}\Rightarrow{/tex} x₁(y₂ - y₃₎ + x₂(y₃ - y₁)+ x₃(y₁ - y₂)=0
{tex}\Rightarrow{/tex} {tex}(-3)(6 - 9) + 7 (9 - 12) +x(12 - 6) =0{/tex}
{tex}\Rightarrow{/tex} {tex}9 - 21 + 6x = 0{/tex}
{tex}\Rightarrow{/tex} {tex}6x = 12 {/tex}
{tex}\Rightarrow{/tex} {tex}x = 2{/tex}

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