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

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

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

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.