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Case study·Standard multi-step (3/5)·No calculator

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

A quadrilateral has vertices A(1,2)A(1,2), B(5,2)B(5,2), C(7,5)C(7,5) and D(3,5)D(3,5).
Total: 4 marks

(a) Compare the coordinate changes AB→\overrightarrow{AB} and DC→\overrightarrow{DC}. (1 mark)

(b) Compare the midpoints of diagonals ACAC and BDBD. (2 marks)

(c) State whether ABCDABCD is a parallelogram, with a reason. (1 mark)

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cbse-math-9.u4.t4-4.case.010

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