JEE Main202522 Jan 2025Evening ShiftMathematicsStraight LinesActual

Let A(6,8), B(10 ,-10 ) and C(-10 , 10 ) , be the vertices of a triangle. If L(a, 9) and G(h, k) be its orthocenter and centroid respectively, then (5 a-3 h+6 k+100 2 ) is equal to ______ -.

Correct answer

Step-by-step solution

aligned & a+0 3 =h a=3 h & 9+0 3 =k k=3 & (h, k)= ( 6+10 -10 3 , 8-10 -10 3 ) & 6+10 -10 =3 h & 10 -10 =3 h-6 & 10( - )=1 & 8-10 +10 3 =k & 100 2 =99 & h= 7 3 & a=7 aligned Now, 5 a-3 h+6 k+100 2 =35-7+18+99=145

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 2026 From 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 2026 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 the triangle PQR is ( , ) , then 9( + ) is equal 2026 Let 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 2026 Let 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 2026 Let 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 2026 Let 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( + ) 2026 Let 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