JEE Main 2023MathematicsStraight LinesMediumNumerical

JEE Main 2023 — Straight Lines Question with Solution

JEE Main 2023 (24 Jan Shift 2)

Question

The equations of the sides AB, BC & CA of a triangle ABC are 2x+y=0, x+py=21a a≠0 and x-y=3 respectively. Let P2,a be the centroid of the triangle ABC, then BC2 is equal to

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Show full solutionCorrect answer: 122
Correct answer
122

Step-by-step explanation

We have,

Since, G2,a, so

1+α+β+33=2 and -2-2α+β3=a

⇒α+β=2 and -2α+β=3a+2

So, α=-a, β=2+a

So, B≡-a,2a, C≡5+a,2+a

Now, B and C lies on the line x+py=21a, so

-a+2pa=21a

⇒p=11

Also,

5+a+112+a=21a

⇒27=9a⇒a=3

So,

B≡-3,6, C≡8,5

So,

BC2=121+1=122

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About this question

This is a previous-year question from JEE Main 2023, 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.