Q. 165.0( 3 Votes )

If the points A(-

Answer :

Given points A(-2, 1), B(a, b) and C(4, -1) 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 =



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


[-2(b – (-1)) + a(-1 – 1) + 4(1 – b)] = 0


[-2(b + 1) -2a + 4(1 – b)] = 0


[-2b -2 -2a + 4 – 4b] = 0


-2a - 6b + 2 = 0


-2a – 6b = -2


Dividing by -2, we get


a + 3b = 1


a = 1- 3b … (2)


Substituting (2) in (1),


(1 – 3b) – b = 1


1 – 4b = 1


4b = 0


b = 0


Substituting value of b in (1),


a - 0 = 1


a = 1


Ans. The values of a and b are 1 and 0 respectively.


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