Find the value of x for which the points (x, – 1), (2, 1) and (4, 5) are collinear.
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.