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

The line 2 x + 3 y = 12 meets the coordinates axes at A and B respectively. The line through 5,5 perpendicular to A B meets the coordinate axes and the line A B at C , D and E respectively. If O is the origin, then the area (in sq. units) of the figure O C E B is equal to

Options

  1. A13 3
  2. B23 3
  3. C11
  4. D7

Correct answer

B. 23 3

Step-by-step solution

The equation of a line passing through P 5,5 and perpendicular to 2 x + 3 y = 12 is y - 5 = 3 2 x - 5 or, 3 x - 2 y - 5 = 0 The coordinates of the point of intersection of 2 x + 3 y - 12 = 0 and 3 x - 2 y - 5 = 0 are E 3,2 . The line 3 x - 2 y - 5 = 0 meets x -axis at C 5 3 , 0 . Now, A r e a  o f  f i g u r e  O C E B = A r e a  o f  Δ A O B - A r e a  o f  Δ A C E = 1 2 O A × O B - 1 2 A C × E L = 1 2 × 6 × 4 - 1 2 × 13 3 × 2 = 23 3  

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