Q. 183.6( 5 Votes )

If the points <sp

Answer :

Given points A(-1, -4), B(b, c) and C(5, -1) are collinear


And 2b + c = 4 … (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


[-1(c – (-1)) + b(-1 – (-4)) + 5(-4 – c)] = 0


[-1(c + 1) + 3b + 5(-4 – c)] = 0


[-c - 1 + 3b - 20 – 5c] = 0


3b – 6c - 21 = 0


3b – 6c = 21


Dividing by 3, we get


b – 2c = 7


b = 7 + 2c … (2)


Substituting (2) in (1),


2(7 + 2c) + c = 4


14 + 4c + c = 4


5c = -10


c = -2


Substituting value of c in (1),


2b + (-2) = 4


2b = 6


b = 3


The values of a and b are 3 and -2 respectively.


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