Points are A(-3, 12), B(7, 6) and C(x, 9) are Collinear. Then:
\(\left(x_1=-3, y_1=12\right),\left(x_2=7, y_2=6\right) \text { and }\left(x_3=x, y_3=9\right)\)
It is given that points A, B and C are Collinear. therefore,
\(x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)=0 \)
\(-3(6-9)+7(9-12)+x(12-6)=0 \)
\(-3(-3)+7(-3)+x(6)=0 \)
\(+9-21+6 x=0 \)
-12 + 6x = 0
6x = 12
\( x=\frac{12}{6}\)
x = 2
Therefore, when x = 2, the given points are Collinear.
