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GATE 2022 CE (CE2) – Question 8

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Consider L1: $2x-3y=5$; L2: $3x+2y=8$; L3: $4x-6y=5$; L4: $6x-9y=6$. Which statement is correct?

  1. L1 is parallel to L2 and L1 is perpendicular to L3
  2. L2 is parallel to L4 and L2 is perpendicular to L1
  3. L3 is perpendicular to L4 and L3 is parallel to L2
  4. L4 is perpendicular to L2 and L4 is parallel to L3

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Show answer and explanation

Correct answer: (D) L4 is perpendicular to L2 and L4 is parallel to L3

Explanation

The slopes of L1,L3,L4 are all 2/3, whereas L2 has slope −3/2. Parallel lines have equal slopes and perpendicular lines have slope product −1.

Therefore L4 is perpendicular to L2 and parallel to L3: **D**.