Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main20249 Apr 2024Morning ShiftMathematicsStraight LinesActual

A ray of light coming from the point P(1,2) gets reflected from the point Q on the x -axis and then passes through the point R(4,3) . If the point S(h, k) is such that PQRS is a parallelogram, then h k^2 is equal to :

Options

  1. A70
  2. B80
  3. C60
  4. D90

Correct answer

A. 70

Step-by-step solution

Image of P wrt x -axis will be P^ (1,-2) equation of line joining P^ R will be y-3= 5 3 (x-4) Above line will meet x -axis at Q where aligned & y =0 x = 11 5 & Q ( 11 5 , 0 ) aligned PQRS is parallelogram so their diagonals will bisects each other aligned & 4+1 2 = 11 5 + h 2 & 2+3 2 = k +0 2 & h = 14 5 & k =5 & hk ^2= 14 5 5^2=70 aligned

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