Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202227 Jun 2022Morning ShiftMathematicsStraight LinesActual

In an isosceles triangle A B C , the vertex A is 6 , 1 and the equation of the base B C is 2 x + y = 4 . Let the point B lie on the line x + 3 y = 7 . If α , β is the centroid ∆ A B C , then 15 α + β is equal to

Options

  1. A51
  2. B39
  3. C41
  4. D49

Correct answer

A. 51

Step-by-step solution

In △ A B C ,   A B = A C Solving 2 x + y = 4   &   x + 3 y = 7 , we get B ≡ 1 , 2 Let C ≡ h , k and as it lies on 2 x + y = 4 so 2 h + k = 4 Now, A B 2 = A C 2 26 = ( h - 6 ) 2 + k - 1 2 ⇒ 26 = h - 6 2 + 3 - 2 h 2 ⇒ 26 = 5 h 2 - 24 h + 45 ⇒ h - 1 5 h - 19 = 0 ⇒ h = 19 5 (as h = 1 rejected) so k = - 18 5 Hence, centroid = 6 + 1 + 19 5 3 , 1 + 2 - 18 5 3 ≡ 18 5 , - 1 5 i.e. 15 α + β = 15 × 17 5 = 51

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