Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202227 Jul 2022Evening ShiftMathematicsStraight LinesActual

The equations of the sides A B , B C and C A of a triangle A B C are 2 x + y = 0 , x + p y = 39 and x - y = 3 respectively and P 2 , 3 is its circumcentre. Then which of the following is NOT true

Options

  1. AA C 2 = 9 p
  2. BA C 2 + p 2 = 136
  3. C32 < area ∆ A B C < 36
  4. D34 < area ∆ A B C < 38

Correct answer

D. 34 < area ∆ A B C < 38

Step-by-step solution

Intersection of 2 x + y = 0   &   x - y = 3 is A 1 , - 2 Perpendicular bisector of A B is y - 3 = 1 2 x - 2 ⇒ x - 2 y + 4 = 0 Take image of A along the perpendicular bisector of A B , we get x - 1 1 = y + 2 - 2 = - 2 9 5 = - 18 5 i.e. x = - 13 5 ,   y = 26 5 B - 13 5 , 26 5 This point lies on the line x + p y = 39 i.e. - 13 5 + p 26 5 = 39 ⇒ - 1 + 2 p = 15 ⇒ p = 8 Solving x + 8 y = 39 and x - y = 3 , we get C 7 , 4 Now A C 2 = 1 - 7 2 + - 2 - 4 2 = 72 = 9 p and A C 2 + p 2 = 72

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