Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202628 January 2026Morning ShiftMathematicsStraight LinesActual

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line x+2 2 y=4 . If the co-ordinates of the vertex A are ( , ) , then the greatest integer less than or equal to | + 2 | is

Options

  1. A2
  2. B5
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

Let ABC be an equilateral triangle with orthocenter at the origin O(0,0) and side BC on the line x + 2 2 y = 4 . Since m_ BC m_ AD = -1 : (- 1 2 2 ) ( ) = -1 = 2 2 ...(1) Distance from O to BC: OD = |-4| 1+8 = 4 3 For equilateral triangle: AO = 8 3 , so AD = 4 3 + 8 3 = 4 | + 2 2 - 4| 3 = 4 = 16 9 or - 8 9 Since A( , ) and O(0,0) lie on the same side of BC (origin gives 0+0-4 ( , ) = (- 8 9 , - 16 2 9 ) | + 2 | = | -8-32 9 | = 40 9 = 4

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and 3x+4y-1=0 , meets the co-ordinate axes at the points P and Q, then the locus of the mid point 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0 . These rays get reflected from the mirror x + 2y = 1 . If the equations of the reflected r 2026In 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 the triangle PQR is ( , ) , then 9( + ) is equal 2026Let P(3 , 2 ) , 0 , be a point on the ellipse x^2 9 + y^2 4 =1 , Q be a point on the circle x^2+y^2-14x-14y+82=0 and R be a point on the line x+y=5 such that the centroid of the tr 2026Let A,B be points on the two half-lines x- 3 |y|= , >0 at a distance of from their point of intersection P . The line segment AB meets the angle bisector of the given half-lines at 2026Let the line L₁ : x + 3 = 0 intersect the lines L₂ : x - y = 0 and L₃ : 3x + y = 0 at the points A and B , respectively. Let the bisector of the obtuse angle between the lines L₂ a 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5, -1) . If the centroid of this triangle is (3, 4) and its circumcenter is ( , ) , then 21( + ) 2026Let the mid points of the sides of a triangle ABC be ( 5 2 , 7 ) , ( 5 2 , 3 ) and (4, 5) . If its incentre is (h, k) , then 3h + k is equal to : 2026 Full Straight Lines list All JEE Main PYQs