Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

The lengths of the perpendiculars from the points m 2 , 2 m , m n , m + n and n 2 , 2 n to the line x + 3 y + 3 = 0 are in

Options

  1. AArithmetic progression
  2. BGeometric progression
  3. CHarmonic progression
  4. DNone of these

Correct answer

B. Geometric progression

Step-by-step solution

The given line is x + 3 y + 3 = 0 … 1 Let p 1 , p 2 and p 3 are the lengths of the perpendiculars from the points A m 2 , 2 m , B m n , m + n and C n 2 , 2 n respectively on the given line, then p 1 = m 2 + 3 2 m + 3 1 + 3 ⇒ m + 3 2 2 p 2 = m n + 3 m + n + 3 1 + 3 ⇒ m + 3 n + 3 2 p 3 = n 2 + 3 2 n + 3 1 + 3 ⇒ n + 3 2 2 Clearly, p 1 . p 3 = p 2 2 ∴ p 1 , p 2 , p 3 are in GP

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 NTA Abhyas JEE Main PYQs