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Question
For what value of y, are the points P(1, 4), Q(3,y) and R(-3, 16) are collinear ?
Solution
P(1, 4), Q(3,y) and R(-3, 16) are the given points. Then:
`(x_1=1, y_1=4), (x_2=3, y_2=y) and (x_3 =-3, y_3 =16)`
It is given that the points P, Q and R are collinear. Therefor,
`x_1 (y_2-y_3) +x_2(y_3-y_1)+x_3(y_1-y_2)=0`
`⇒ 1(y-16)+3(16-4)+(-3)(4-y)=0`
`⇒ 1(y-16)+3(12)-3(4-y)=0`
`⇒ y-16+36-12+3y=0`
`⇒8+4y=0`
`⇒ 4y =-8/4=-2`
When, y=-2 the given points are collinear.
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