Question

A ray of light passing through the point \( (1, 2) \) is reflected on the \( x \)-axis at a point \( P \) and passes through the point \( (5, 6) \). Then the abscissa of the point \( P \) is:

• A. 3
• B. \( \frac{5}{2} \)
• C. 2
• D. 4
• E. \( \frac{3}{2} \)

Hint:

Reflection in the \( x \)-axis flips the \( y \)-coordinate, helping determine intersection points.

Answer 1

The Correct Option is C

To find the abscissa of point \( P \), we first determine the equation of the line connecting points \( (1, 2) \) and \( (5, 6) \). 
The slope of this line is: \[ m = \frac{6 - 2}{5 - 1} = 1 \] The equation of the line is: \[ y - 2 = 1(x - 1) \quad \Rightarrow \quad y = x + 1 \] Now, since the point \( P \) is on the \( x \)-axis, its \( y \)-coordinate is 0. 
Substituting \( y = 0 \) into the equation of the line: \[ 0 = x + 1 \quad \Rightarrow \quad x = -1 \] Thus, the abscissa of the point \( P \) is 2.