JEE Main 2023MathematicsStraight LinesEasyMCQ

JEE Main 2023 — Straight Lines Question with Solution

JEE Main 2023 (15 Apr Shift 1)

Question

If α, β is the orthocenter of the triangle ABC with vertices A3, –7, B–1, 2 and C4, 5, then 9α-6β+60 is equal to

Choose an option

Show full solutionCorrect option: A
Correct answer
A25

Step-by-step explanation

The required diagram will be: 

Equation of AD:y+7=-53x-3

⇒3y+21=-5x+15

⇒5x+3y+6=0 ......i

Equation of BE:y-2=-112x+1

⇒12y-24=–x-1

⇒x=23-12y....(ii)

by ii 115-60y+3y+6=0

⇒57y=121

y=12157, x=23-12×12157

∴ 9α-6β+60=9×23-108×12157-6×12157+60

=207-242+60=25

Hence this is the required option.

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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.