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

Let the incentre of Δ A B C is Ι 2,5 . If A = 1,13 and B = - 4,1 , then the coordinates of C are

Options

  1. A1,10
  2. B10,1
  3. C8,2
  4. D9,3

Correct answer

B. 10,1

Step-by-step solution

Slope of A B is 13 - 1 1 - - 4 = 12 5 Slope of B I is 5 - 1 2 - - 4 = 2 3 Slope of A I is 13 - 5 1 - 2 = - 8 Let, the slopes of B C and A C are m 1 & m 2 respectively ⇒ m 2 - - 8 1 + m 2 - 8 = - 8 - 12 5 1 + - 8 12 5 m 2 + 8 91 = 1 - 8 m 2 - 57 8 × 91 - 57 = 8 × 57 - 91 m 2 ⇒ m 2 = - 4 3 Now, m 1 - 2 3 1 + m 1 2 3 = 2 3 - 12 5 1 + 2 3 × 12 5 ⇒ 3 m 1 - 2 39 = 3 + 2 m 1 - 26 ⇒ 9 m 1 - 6 = - 6 - 4 m 1 ⇒ m 1 = 0 ⇒ The equation of A C is y - 13 = - 4 3 x - 1 and the equation of B C is y = 1 ⇒ C is 10,1

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