Geometric transformations (rotation) — KCSE Mathematics

KCSE Mathematics · 90 practice questions · 3 syllabus objectives

25 easy33 medium32 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Rotate a point or shape through a given angle (90°, 180°, 270°) about a given centre of rotation

Determine the centre, angle and direction of rotation given an object and its image

Geometric transformations (rotation)

Sample Questions

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1
easySHORT ANSWER3 marks

State how to determine the centre of rotation when a quadrilateral PQRS with vertices P(1, 1), Q(3, 1), R(3, 3), and S(1, 3) is rotated to form quadrilateral P'Q'R'S' with vertices P'(1, 3), Q'(3, 3), R'(3, 1), and S'(1, 1). (3 marks)

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Part (a) — 3 marks
Join points P and P' and construct the perpendicular bisector (1 mk)
Join points Q and Q' and construct the perpendicular bisector (1 mk)
The intersection of the two bisectors gives the centre of rotation (1 mk)
2
easySHORT ANSWER4 marks

State the centre of rotation and the angle of rotation when triangle ABC with vertices A(2, 3), B(4, 5), and C(6, 3) is rotated to form triangle A'B'C' with vertices A'(3, 2), B'(5, 4), and C'(3, 6). (4 marks)

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Part (a) — 4 marks
Centre of rotation is (4, 4) (1 mk)
Angle of rotation is 90° (1 mk)
Direction of rotation is clockwise (1 mk)
Coordinates of A'B'C' confirm the transformation (1 mk)
3
easySHORT ANSWER2 marks

A point B(3, 4) is rotated about the origin through an angle of +180°. State the coordinates of the image B′. (2 marks)

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Part (a) — 2 marks
For +180° about the origin: (x, y) → (−x, −y) (1 mk)
B′ = (−3, −4) (1 mk)
4

Identify the coordinates of the image of triangle ABC with vertices A(1, 1), B(2, 3), and C(3, 1) after a rotation of 180° about the origin. (3 marks)

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