FRQ — Coordinate Geometry

Case study·Hard exam skill (4/5)·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 triangular walking path on a grid has vertices

A(0,0)

B(8,0)

, and

C(8,6)

. A bench is to be placed at the midpoint of the direct path from

A

C

Total: 5 marks

(a) Find $AB$ , $BC$ , and $AC$ . (2 marks)

(b) Explain why the angle at $B$ is a right angle. (1 mark)

(d) How much longer is the route $A\to B\to C$ than the direct route $A\to C$ ? (1 mark)

Your response (optional — you can also work on paper)

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