Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Straight Lines

The vertices of a triangle are A(-1,3), B(-2,2) and C(3,-1) . A new...

The vertices of a triangle are A(−1,3),B(−2,2)\mathrm{A}(-1,3), \mathrm{B}(-2,2) and C(3,−1)\mathrm{C}(3,-1). A new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :The vertices of a triangle are A(-1,3), B(-2,2) and C(3,-1) . A new triangle is formed by shifting the sides of the

Options

  1. Ax+y+(2−2)=0x+y+(2-\sqrt{2})=0
  2. B−x+y−(2−2)=0-x+y-(2-\sqrt{2})=0
  3. Cx+y−(2−2)=0x+y-(2-\sqrt{2})=0
  4. Dx−y−(2+2)=0x-y-(2+\sqrt{2})=0

Correct answer

C. x+y−(2−2)=0x+y-(2-\sqrt{2})=0

Step-by-step solution

The vertices of a triangle are A(-1,3), B(-2,2) and C(3,-1) . A new triangle is formed by shifting the sides of the
equation of AC→x+y=2\mathrm{AC} \rightarrow \mathrm{x}+\mathrm{y}=2 equation of line parallel to ACx+\mathrm{AC} \mathrm{x}+\mathrm{y}=\mathrm{d}∣d−22∣=1 d=2−2\begin{aligned} & \left|\frac{\mathrm{d}-2}{\sqrt{2}}\right|=1 \\ & \mathrm{~d}=2-\sqrt{2} \end{aligned}eqn\mathrm{eq}^{\mathrm{n}} of new required line x+y=2−2\mathrm{x}+\mathrm{y}=2-\sqrt{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… JEE Main 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0… JEE Main 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along… JEE Main 2026Let P(3 α, 2 α) , α ≠ 0 , be a point on the ellipse (x^2)/(9)+(y^2)/(4)=1 , Q be a point… JEE Main 2026Let A,B be points on the two half-lines x- 3 |y|=α , α>0 at a distance of α from their… JEE Main 2026Let the line L_1 : x + 3 = 0 intersect the lines L_2 : x - y = 0 and L_3 : 3x + y = 0 at… JEE Main 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5… JEE Main 2026Let the mid points of the sides of a triangle ABC be ((5)/(2), 7) , ((5)/(2), 3) and (4… JEE Main 2026Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the… JEE Main 2026Let the angles made with the positive x -axis by two straight lines drawn from the point… JEE Main 2026Let A(1,0), B(2,-1) and C((7)/(3), (4)/(3)) be three points. If the equation of the… JEE Main 2026Let A(1,2) and C(-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD… JEE Main 2026A rectangle is formed by the lines x=0, y=0, x=3 and y=4 . Let the line L be… JEE Main 2026Among the statements (S 1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose… JEE Main 2026Let a point A lie between the parallel lines L_ 1 and L_ 2 such that its distances from… JEE Main 2026A line passing through the point P(a, θ) makes an acute angle α with the positive x… JEE Main 2025 Full Straight Lines list Straight Lines JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs