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QJEEM24Ma2ea1: JEE Main 2024 Mathematics - Class 11 JEEM24Ma2ea1 Solution: A ray of light coming from the point gets reflected from the…

A ray of light coming from the point P(1,2)\mathrm{P}(1,2) gets reflected from the point Q\mathrm{Q} on the xx -axis and then passes through the point R(4,3)R(4,3) . If the point S(h,k)S(h, k) is such that PQRSP Q R S is a parallelogram, then hk2hk^2 is equal to:

Multiple Choice Options

  • A 60
  • B 70
  • C 80
  • D 90

Step-by-Step Verified Solution

JEE Main 2024 (Online) 9th April Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 19 English Explanation

amp;P′R:y+2=53(x−1)amp; For Point Q⇒y=0amp;65=a−1⇒a=115\begin{aligned}& P^{\prime} R: y+2=\frac{5}{3}(x-1) \\& \text { For Point } Q \Rightarrow y=0 \\& \frac{6}{5}=a-1 \Rightarrow a=\frac{11}{5}\end{aligned}

Now, PQRSP Q R S is parallelogram

amp;∴h+a2=4+12⇒h=5−115=145amp; and 2+32=k2⇒K=5\begin{aligned}& \therefore \frac{h+a}{2}=\frac{4+1}{2} \Rightarrow h=5-\frac{11}{5}=\frac{14}{5} \\& \text { and } \frac{2+3}{2}=\frac{k}{2} \Rightarrow K=5\end{aligned}

Now hk2=25×145=14×5=70h k^2=25 \times \frac{14}{5}=14 \times 5=70

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