Mathematics · Straight lines

JEE Main 2026 — 5 April, Morning Shift — Question 34

In an equilateral triangle PQR, let the vertex P be at $(3,5)$ and the side QR be along the line $x+y=4.$ If the orthocentre of triangle $PQR$ is $(α,β),$ then $9(α+β)$ is equal to :

Option A:
$16$
Option B:
$27$
Option C:
$36$
Option D:
$48$
Correct

Answer: D

Step-by-step solution

$\mathrm{Q}: \frac{\mathrm{x}-3}{1}=\frac{\mathrm{y}-5}{1}=-\frac{(3+5-4)}{1+1}$ Q(1, 3) So orthocentre is $\left(\frac{2+3}{3}, \frac{6+5}{3}\right)$ $\left(\frac{5}{3}, \frac{11}{3}\right)$ So $9(\alpha+\beta)=3(16)=48$

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Exam: JEE Main 2026
Paper: 5 April, Morning Shift
Subject: Mathematics
Chapter: Straight lines
Topic: Cartesian Coordinates and Basic Coordinate Geometry