Q. 205.0( 3 Votes )

If the points <sp

Answer :

Given points P(-3, 9), Q(a, b) and R(4, -5) are collinear


And a + b = 1 … (1)


We have to find the values of a and b.


Since the given points are collinear, the area of the triangle formed by them must be 0.


We know that the area of Triangle =


= 0


[x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = 0


[-3(b – (-5)) + a(-5 – 9) + 4(9 – b)] = 0


[-3(b + 5) -14a + 4(9 – b)] = 0


[-3b – 15 - 14a + 36 – 4b] = 0


-14a - 7b + 21 = 0


-14a – 7b = -21


Dividing by -7, we get


2a + b = 3


b = 3 – 2a … (2)


Substituting (2) in (1),


a + (3 – 2a) = 1


-a + 3 = 1


-a = -2


a = 2


Substituting value of a in (1),


2 + b = 1


b = -1


The values of a and b are 2 and -1 respectively.


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