Question

For what value of x are the points (1,5), (x,1) and (4,11) collinear?
1. 1
2. 2
3. 3
4. -1

Answer 1

Correct Answer - Option 4 : -1

Calculation:

Area of the triangle formed by given points

= \(\frac{1}{2}\) |1(1-11) + x(11-5) + 4(5-1)|

= \(\frac{1}{2}\)|6x + 6|

= 3 |x + 1|

The given points are collinear iff area of triangle = 0

i.e, iff 3 |x + 1| = 0

i.e, x + 1 = 0 iff x = -1

Hence the required value of x is -1.