JEE Main 2022MathematicsStraight LinesHardNumerical

JEE Main 2022 — Straight Lines Question with Solution

JEE Main 2022 (28 Jun Shift 1)

Question

A ray of light passing through the point P2,3 reflects on the X-axis at point A and the reflected ray passes through the point Q5,4. Let R be the point that divides the line segment AQ internally into the ratio 2:1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be α,β. Then, the value of 7α+3β is equal to _____.

Enter your answer

Show full solutionCorrect answer: 31
Correct answer
31

Step-by-step explanation

By observation we know the point Aα,0 and β=y-coordinate of R=2×4+1×02+1=83     ⋯1

Now P' is image of P in y=0 which will be P'2,-3

∴  Equation of P'Q is y+3=4+35-2x-2 

i.e. 3y+9=7x-14

Now P'Q meets x-axis at A

so A≡237,0 by solving with y=0

∴α=237     ⋯2

By 1,2, we get

7α+3β=23+8=31

Practice this on the real CBT interface

Solve this JEE Main question (and the rest of the Straight Lines chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.

Solve interactively →

About this question

This is a previous-year question from JEE Main 2022, covering the Straight Lines chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.