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Question
Find the value of y for which the points A(-3, 9), B(2,y) and C(4,-5) are collinear.
Solution
Let `A(x_1=-3,y_1=9),B(x_2=2,y_2=y) and C(x_3=4, y_3=-5)` be the given points
The given points are collinear if
`x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_2-y_2)=0`
`⇒(-3)(y+5)+2(-5-9)+4(9-y)=0`
`⇒ -3y-15-28+36-4y=0`
⇒7y = 36-43
⇒y = -1
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