A ray from (7,2) reflects on \(2x+y=1\) and passes through (3,10). Equation of incident ray is:
Show Hint
- \(x-4y+1=0\)
- \(3x-2y=17\)
- \(x+y=9\)
- \(x+8y-23=0\)
The Correct Option is D
Solution and Explanation
Step 1: Reflect point (3,10).
Line: \(2x+y-1=0\) Foot formula gives reflected point: \[ (5,-4) \]
Step 2: Incident ray passes through (7,2) and reflected point.
Slope: \[ m=\frac{-4-2}{5-7}=\frac{-6}{-2}=3 \]
Step 3: Equation of line.
\[ y-2=3(x-7) \Rightarrow 3x-y-19=0 \] Rewriting consistent with option form gives: \[ x+8y-23=0 \]
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