Question

The points (x,-1), (2,1) and (4,5) are collinear. Then, x = .

• A. 1
• B. 0.0
• C. 2
• D. -1

Answer 1

The correct option is A 1

Let the points be A(x,-1), B(2,1), C(4,5)
If these three points are collinear
Then
Slope of line AB = slope of line BC
$Slope=\frac{y_2-y_1}{x_2-x_1}$
$\Rightarrow \frac{1+1}{2-x}=\frac{5-1}{4-2}$
$\Rightarrow \frac{2}{2-x}=\frac{4}{2}$
$\Rightarrow \frac{2}{2-x}=2$
$\Rightarrow 2-x=1$
$\Rightarrow x=1$