JEE Main 2021 · 26 February · morning · Single correct · +4 / −1

The intersection of three lines x - y = 0, x + 2y = 3 and 2x + y = 6 is a :

  1. (a) Right angled triangle
  2. (b) Equilateral triangle
  3. (c) None of the above
  4. (d) Isosceles triangle
Answer and solution

Answer (d) Isosceles triangle

Solution

Maths sir · 3 steps

Find the three corners, then compare the side lengths: two of them come out equal.

  1. Find the vertices. Solve the lines in pairs. x - y = 0 with x + 2y = 3 gives (1, 1). x - y = 0 with 2x + y = 6 gives (2, 2). x + 2y = 3 with 2x + y = 6 gives (3, 0).
    SideLength squaredLength
    (1,1) to (2,2)1² + 1² = 2√2
    (1,1) to (3,0)2² + 1² = 5√5
    (2,2) to (3,0)1² + 2² = 5√5
  2. Check for right angle. For a right angle, the largest squared side must equal the sum of the other two. Here 5 ≠ 2 + 5, so no angle is 90°.
  3. So. Two sides are equal (√5 each) and the third is √2, so the triangle is isosceles, option (d).

The idea to keep. Get the three vertices and compare side lengths. Shortcut: if two lines are mirror images in the third, like x + 2y = 3 and 2x + y = 6 in y = x, the triangle is isosceles.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Straight Lines

Asked about 130 times in JEE Main since 2020. This question is from 2021.