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Question
If the points P(-3, 9), Q(a, b) and R(4, -5) are collinear and a+b=1, find the value of a and b.
Solution
`"Let "A(x_1=3,y_1=9) ,B(x_2=a,y_3=b) and C(x_3=4,y=-5)`be the given points
The given pots are collinear if
`x_1 (y_2-y_3)+x_3 (y_3-y_1)+x_3 (y_1-y_2) =0`
`⇒ (-3)(b+5)+a(-5-9)+4(9-b)=0`
`⇒-3b-15-14a+36-4b=0`
⇒ 2a + b = 3
Now solving 1 a +b = 1 and 2a+ b = 3, we get a =2 and b= -1.
Hence, a = 2 and b = -1.
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