Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2025 · 29 January · Morning Shift · Mathematics · Straight Lines

Let A B C be a triangle formed by the lines 7 x-6 y+3=0, x+2 y-31=0...

Let ABCA B C be a triangle formed by the lines 7x−6y+3=0,x+2y−31=07 x-6 y+3=0, x+2 y-31=0 and 9x−2y−19=09 x-2 y-19=0. Let the point (h,k)(h, k) be the image of the centroid of (\Delta A B C) in the line 3x+6y−53=03 x+6 y-53=0. Then h2+k2+hkh^2+k^2+h k is equal to:

Options

  1. A47
  2. B37
  3. C36
  4. D40

Correct answer

B. 37

Step-by-step solution

∴ centroid of  △ABC=(9+3+53,11+4+133)=(173,283)\begin{aligned} \therefore \text{ centroid\text{ of } } \triangle \mathrm{ABC} & =\left(\frac{9+3+5}{3}, \frac{11+4+13}{3}\right) \\ & =\left(\frac{17}{3}, \frac{28}{3}\right)\end{aligned} Let image of centroid with respect to line mirror is (h,k)∴(k−283h−173)(−12)=−13(h+1732)+6⋅(k+2832)=53\begin{aligned} & (\mathrm{h}, \mathrm{k}) \\ & \therefore\left(\frac{\mathrm{k}-\frac{28}{3}}{\mathrm{ h}-\frac{17}{3}}\right)\left(-\frac{1}{2}\right)=-1 \\ & & 3\left(\frac{\mathrm{ h}+\frac{17}{3}}{2}\right)+6 \cdot\left(\frac{\frac{\mathrm{k}+28}{3}}{2}\right)=53 \end{aligned} Solving (1) \& (2) we get $\mathrm{h}=3, \mathrm{k}=4 \therefore \mathrm{h}^2+\mathrm{k}^2+\mathrm{hk}=37
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… JEE Main 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0… JEE Main 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along… JEE Main 2026Let P(3 α, 2 α) , α ≠ 0 , be a point on the ellipse (x^2)/(9)+(y^2)/(4)=1 , Q be a point… JEE Main 2026Let A,B be points on the two half-lines x- 3 |y|=α , α>0 at a distance of α from their… JEE Main 2026Let the line L_1 : x + 3 = 0 intersect the lines L_2 : x - y = 0 and L_3 : 3x + y = 0 at… JEE Main 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5… JEE Main 2026Let the mid points of the sides of a triangle ABC be ((5)/(2), 7) , ((5)/(2), 3) and (4… JEE Main 2026Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the… JEE Main 2026Let the angles made with the positive x -axis by two straight lines drawn from the point… JEE Main 2026Let A(1,0), B(2,-1) and C((7)/(3), (4)/(3)) be three points. If the equation of the… JEE Main 2026Let A(1,2) and C(-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD… JEE Main 2026A rectangle is formed by the lines x=0, y=0, x=3 and y=4 . Let the line L be… JEE Main 2026Among the statements (S 1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose… JEE Main 2026Let a point A lie between the parallel lines L_ 1 and L_ 2 such that its distances from… JEE Main 2026A line passing through the point P(a, θ) makes an acute angle α with the positive x… JEE Main 2025 Full Straight Lines list Straight Lines JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs