A ray of light passing through the point B (1, 2) reflects on the x-axis at point A and the reflected ray passed through the point C (5, 3). Find the coordinates of the point A.
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Let the point A be (a,0).
Equation of line BA : (y - 2)/ (x -1) = (2-0)/(1-a)
Slope of the line BA = m = 2/(1-a)
The slope of the reflected ray from x axis = slope of line AC = -m
Hence, -2/(1-a) = (3-0)/(5-a)
2a-10 = 3 - 3a
a = 13/5
Point A = (13/5, 0)
Equation of line BA : (y - 2)/ (x -1) = (2-0)/(1-a)
Slope of the line BA = m = 2/(1-a)
The slope of the reflected ray from x axis = slope of line AC = -m
Hence, -2/(1-a) = (3-0)/(5-a)
2a-10 = 3 - 3a
a = 13/5
Point A = (13/5, 0)
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