Answer :

The given points (x, – 1), (2, 1) and (4, 5) are collinear.

To Find: The value of x.


Concept Used: It is given that points are collinear, SO the area of the triangle formed by the points must be zero.


Formula used: The area of triangle = x1(y1 – y3) + x2(y3 – y1) + x3(y1 – y2)


Explanation: Let be points of triangle A(x, – 1), B(2, 1) and C(4, 5)


Now, The points are collinear than, Area of a triangle is zero.


Here, Put the given values in formula and we get,


x(1 – 5) + (2)(5 – (– 1)) + 4(– 1 – 1) = 0


x – 5x + 12 – 8 = 0


– 4x + 4 = 0


4x = 4


x = 1


Hence, The value of x is 1.


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