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Question
For what value of x are the points A(-3, 12), B(7, 6) and C(x, 9) collinear.
Solution
A(-3,12) ,B (7,6) and C(x,9) are the given points. Then:
`(x_1=-3,y_1=12) , (x_2=7,y_2=6) and (x_3= x, y_3=9)`
It is given that points A, B and C are collinear. Therefore,
`x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)=0`
`⇒ (-3)(6-9)+7(9-12)+x(12-6)=0`
`⇒(-3)(-3)+7(-3)+x(6)=0`
`⇒ 9-21+6x=0`
`⇒ 6x-12=0`
`⇒ 6x =12`
`⇒ x = 12/6=12`
Therefore, when x =2 , the given points are collinear
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