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A ray of light passes through the point A(1, 2) and is reflected at a point B on the x-axis. The reflected ray passes through the point (5, 3). Find the equation of line AB.
- 5x + 4y = 13
- 5x - 4y = -3
- 4x + 5y = 14
- 4x - 5y = -6
Correct answer: 5x - 4y = -3
Solution
Reflect A(1,2) over x-axis: A' = (1,-2). Line through A'(1,-2) and C(5,3): slope m = (3+2)/(5-1) = 5/4. Equation: y+2 = (5/4)(x-1) => 4y+8 = 5x-5 => 5x-4y = 13. Set y=0: 5x = 13 => x = 13/5. So B = (13/5, 0). Line AB: through A(1,2) and B(13/5,0). Slope = (0-2)/(13/5-1) = -2/(8/5) = -10/8 = -5/4. Equation: y-2 = (-5/4)(x-1) => 4y-8 = -5x+5 => 5x+4y = 13. That gives 5x+4y = 13.
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