Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Highly selective Backlog Qs for JEE MainMathematicsStraight Lines

The area of a triangle is 5. If two of its vertices are 2 , 1 ,   3 , - 2 and the third vertex lies on the line y = x + 3 , then the third vertex is -

Options

  1. A- 7 2 , - 13 2
  2. B- 7 2 , 13 2
  3. C7 2 , - 13 2
  4. D7 2 , 13 2

Correct answer

D. 7 2 , 13 2

Step-by-step solution

Let the third vertex be h ,   k Since it lies on line y = x + 3 ∴   k = h + 3 ........(1) Also area of triangle is 5 ∴ 1 2 2 - 2 - k + 3 k - 1 + h   1 + 2 = ±   5 ⇒ k + 3 h -   7 = ±   10 ........(2) Solving (1) & (2) we get h = 7 2 ,   k   = 13 2 ⇒   7 2 , 13 2 and h = - 3 2 ,   k = 3 2 ⇒   - 3 2 , 3 2

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 Highly selective Backlog Qs for JEE Main PYQs