Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainMathematicsStraight Lines

A rectangular region in the Cartesian plane is defined by the inequalities |x - 3| 2 and |y + 1| 4 . A line L is parallel to the line 3x - 4y + 5 = 0 and divides the area of the rectangular region into two equal parts. The perpendicular distance of the point (-2, 4) from the line L is equal to :

Options

  1. A27 5
  2. B1
  3. C7
  4. D22 5

Correct answer

C. 7

Step-by-step solution

The given inequalities |x - 3| 2 and |y + 1| 4 represent a rectangle centered at the point (3, -1) . Any line that divides the area of a rectangle into two equal parts must pass through its geometric center. Therefore, the line L passes through (3, -1) . The line L is parallel to 3x - 4y + 5 = 0 , which has a slope of 3 4 . Thus, the slope of line L is also 3 4 . The equation of line L is: y - (-1) = 3 4 (x - 3) 4(y + 1) = 3(x - 3) 4y + 4 = 3x - 9 3x - 4y - 13 = 0 The perpendicular distance d of the point (-2, 4) f

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