Misc 22 - A ray of light passing through (1, 2) reflects on x-axis - Miscellaneous

  1. Chapter 10 Class 11 Straight Lines
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Misc 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. There is a point A on x-axis on which ray reflects A ray passing through P(1, 2) reflects on point A On reflection, the ray passes through point Q(5, 3) We need to find coordinate of A Since point A is on the x-axis, its y-coordinate is 0 Let coordinates of point A be (k, 0) So, we need to find value of k We need to find angle with positive x-axis of both lines Line QA makes angle ∠ QAX with positive x-axis Line PA makes ∠ PAX with positive x-axis Let ∠ QAX = θ Now, MA is normal ∠ MAX = 90° θ + ∠ MAQ = 90° ∠ MAQ = 90° – θ Also, ∠ MAP = ∠ MAQ = 90 – θ Now, ∠ PAX = ∠ MAP + ∠ MAQ + ∠ QAX = (90 – θ) + (90 – θ) + θ = 180 – θ Now, we find slope of line PA & QA We know that slope of line that passes through points (x1, y1) & (x2, y2) is m = (𝑦_2 − 𝑦_1)/(𝑥_2 − 𝑥_1 ) From (1) & (2) 2/(𝑘 − 1) = ( − 3)/(𝑘 − 5) 2(k − 5) = − 3(k − 1) 2k − 10 = − 3k + 3 2k + 3k = 3 + 10 5k = 13 k = 13/5 Hence point A (13/5, 0)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.