Class 10

Math

All topics

Coordinate Geometry

For what value of x are the points $A(−3,12)$, $B(7,6)$ and $C(x,9)$ collinear?

Points are $A(−3,12),B(7,6)$ and $C(x,9)$ are collinear.

Which means area of triangle ABC$=0$

Area of a triangle $=21 [x_{1}(y_{2}−y_{3})+x_{2}(y_{3}−y_{1})+x_{3}(y_{1}−y_{2})]$

$=21 [−3(6−9)+7(9−12)+x(12−6)]$

$=21 [−3×(−3)+7×(−3)+x×6]$

$=21 [9−21+6x]$

$=21 [6x−12]$

Since points are collinear:

$21 (6x−12)=0$

or $x=2$.