Last updated at Dec. 8, 2016 by Teachoo

Transcript

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 = Now, MA is normal MAX = 90 + MAQ = 90 MAQ = 90 Also, MAP = MAQ = 90 Now, PAX = MAP + MAQ + QAX = (90 ) + (90 ) + = 180 Now, we find slope of line PA & QA We know that slope of line that passes through points (x1, y1) & (x2, y2) is m = ( _2 _1)/( _2 _1 ) From (1) & (2) 2/( 1) = ( 3)/( 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)

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.