Question

The value of x, for which the points (x,-1), (2,1) and (4,5) lie on a line is

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is C 1

The condition for the three points to lie on a straight line is that the area of the triangle formed by these three points is zero.
Area of a triangle = 0
$\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$ = 0

$\Rightarrow$ x(1 - 5) + 2(5 + 1) + 4 (-1-1) = 0

$\Rightarrow$x - 5x + 10 + 2 - 4 - 4 = 0

$\Rightarrow$ -4x + 12 - 8 = 0

$\Rightarrow$-4x+4=0

$\Rightarrow$x=1