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GATE CSE 2022 Q9: Placing letters at corners and mid-points of a triangle

Question

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:

• The line joining P and R is parallel to the line joining Q and S. • P is placed on the side opposite to the corner T. • S and U cannot be placed on the same side.

Which one of the following statements is correct based on the above information?

Try it: multiple choice: exactly one correct option

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Wrong answer costs 2/3 mark in GATE.
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Answer: B (official GATE 2022 final answer key)

Concept used: In a triangle, a line through two mid-points is parallel to the third side (mid-point theorem); every side holds two corners and one mid-point.

First step: Each side of the triangle contains two corners, so a corner shares a side with every other point except the opposite mid-point; use this with the S and U condition.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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