Question
Question: A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected fr...
A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected from the point P on x-axis. If the reflected ray passes through the point (6, 4), then the co-ordinates of P are
A
(26/7, 0)
B
(0, 26/7)
C
(-26/7, 0)
D
(-3, 0)
Answer
(26/7, 0)
Explanation
Solution
Reflect the point (2, 3) across the x-axis to get (2, -3). The line connecting (2, -3) and (6, 4) intersects the x-axis at point P. The equation of the line is y - 4 = ((4 - (-3))/(6 - 2))(x - 6). Substituting y = 0, we get -4 = (7/4)(x - 6), which gives x = 26/7. Thus, P is (26/7, 0).