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A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A
Solution:
We can see the scenario of the given problem in the following figure.
Let the coordinates of point A be (a, 0).
Draw a line, AL perpendicular to the x-axis
We know that angle of incidence is equal to angle of reflection.
Hence, let ∠BAL = ∠CAL = Φ and ∠CAX = θ
Now,
∠OAB = 180° - (θ + 2Φ)
= 180° - [θ + 2 (90° - θ)]
= 180° - [θ + 180° - 2θ]
= 180° - 180° + θ
= θ
Therefore,
∠BAX = 180° - θ
Now,
Slope of line AC = (3 - 0)/(5 - a)
⇒ tanθ = 3/(5 - a) ....(1)
⇒ Slope of line AB = (2 - 0)/(1 - a)
⇒ tan (180° - θ) = 2/(1 - a)
⇒ tanθ = 2/(1 - a) ....(2)
From equations (1) and (2), we obtain
⇒ 3/(5 - a) = 2/(1 - a)
⇒ 3a - 3 = 10 - 2a
⇒ a = 13/5
Thus, the coordinates of point A are (13/5, 0)
NCERT Solutions Class 11 Maths Chapter 10 Exercise ME Question 22
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A
Summary:
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Then the coordinates of A are (13/5, 0)
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