Question

A ray of light passing through the point (2, 3) reflects on the Y-axis at a point P. If the reflected ray passes through the point (3, 2) and P = (a, b), then 5b = ?

• A. \(a - 5\)
• B. \(a - 13\)
• C. \(a + 13\)
• D. \(a + 5\)

Hint:

Remember that when a point is reflected on the Y-axis, the x-coordinate changes sign and the y-coordinate remains the same.

Answer 1

The Correct Option is C

Step 1: Understand the reflection property. When a ray of light reflects on the Y-axis, the x-coordinate of the incident ray changes sign, while the y-coordinate remains the same.
Let the incident point be A(2, 3) and the reflected point be B(3, 2).
Let the point of reflection on the Y-axis be P(a, b). Since P is on the Y-axis, a = 0.

Step 2: Use the reflection property to find the image of A.
The image of A(2, 3) with respect to the Y-axis is A'(-2, 3).

Step 3: Use the fact that A', P, and B are collinear.
Since A', P, and B are collinear, the slope of A'P is equal to the slope of PB.
Slope of A'P = \(\frac{b - 3}{a - (-2)} = \frac{b - 3}{a + 2}\)
Slope of PB = \(\frac{2 - b}{3 - a}\)
Since a = 0,
Slope of A'P = \(\frac{b - 3}{2}\)
Slope of PB = \(\frac{2 - b}{3}\)
Equating the slopes:
\(\frac{b - 3}{2} = \frac{2 - b}{3}\)
3(b - 3) = 2(2 - b)
3b - 9 = 4 - 2b
5b = 13

Step 4: Find the relationship between a and b. Since a = 0, we can write:
5b = 0 + 13
5b = a + 13
Therefore, 5b = a + 13.