Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202429 Jan 2024Evening ShiftMathematicsStraight LinesActual

Let A be the point of intersection of the lines 3 x + 2 y = 14 , 5 x - y = 6 and B be the point of intersection of the lines 4 x + 3 y = 8 , 6 x + y = 5 . The distance of the point P ( 5 , - 2 ) from the line A B is

Options

  1. A13 2
  2. B8
  3. C5 2
  4. D6

Correct answer

D. 6

Step-by-step solution

Solving lines L 1 ( 3 x + 2 y = 14 ) and L 2 ( 5 x - y = 6 ) . ⇒ x = 14 - 2 y 3 = 6 + y 5 ⇒ 70 - 10 y = 18 + 3 y ⇒ 52 = 13 y ⇒ y = 4 ⇒ x = 14 - 8 3 = 2 ⇒ A ≡ 2 , 4 Now, solving lines L 3 ( 4 x + 3 y = 8 ) and L 4 ( 6 x + y = 5 ) ⇒ x = 8 - 3 y 4 = 5 - y 6 ⇒ 48 - 18 y = 20 - 4 y ⇒ 28 = 14 y ⇒ y = 2 ⇒ x = 8 - 6 4 = 1 2 ⇒ B ≡ 1 2 , 2 So, equation of A B is given by, A B : y - 4 = 2 - 4 1 2 - 2 x - 2 ⇒ A B : y - 4 = 4 3 x - 2 ⇒ A B : y - 4 = 4 3 x - 2 ⇒ 3 y - 12 = 4 x - 8 ⇒ 4 x - 3 y + 4 = 0 The distance of P 5 , - 2 fr

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