Geometric transformations (enlargement) — KCSE Mathematics

KCSE Mathematics · 86 practice questions · 3 syllabus objectives

26 easy34 medium26 hard

What You'll Learn

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

Enlarge a shape by a given scale factor from a given centre of enlargement; find the image coordinates

Calculate the scale factor and locate the centre of enlargement given an object and its image; state the ratio of areas

Geometric transformations (enlargement)

Sample Questions

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easySHORT ANSWER4 marks

A square has vertices A(1, 1), B(1, 3), C(3, 3), and D(3, 1). It is enlarged by a scale factor of 0.5 about the point (2, 2). (a) State the coordinates of the image of point A'. (b) Find the coordinates of point B' after the enlargement. (c) What are the coordinates of point D' after the enlargement? (4 marks)

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Part (a) — 1 mark

A' = (2 + 0.5(1 - 2), 2 + 0.5(1 - 2)) = (1.5, 1.5) (1 mk)

Part (b) — 1 mark

B' = (2 + 0.5(1 - 2), 2 + 0.5(3 - 2)) = (1.5, 2.5) (1 mk)

Part (c) — 2 marks

D' = (2 + 0.5(3 - 2), 2 + 0.5(1 - 2)) = (2.5, 1.5) (2 mks)

easySHORT ANSWER4 marks

A triangle has vertices P(3, 2), Q(5, 4), and R(4, 1). It is enlarged by a scale factor of 2 about the point (2, 2). (a) State the coordinates of the image of point P'. (b) Find the coordinates of point Q' after the enlargement. (c) What are the coordinates of point R' after the enlargement? (4 marks)

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Part (a) — 1 mark

P' = (2 + 2(3 - 2), 2 + 2(2 - 2)) = (4, 2) (1 mk)

Part (b) — 1 mark

Q' = (2 + 2(5 - 2), 2 + 2(4 - 2)) = (8, 6) (1 mk)

Part (c) — 2 marks

R' = (2 + 2(4 - 2), 2 + 2(1 - 2)) = (6, 0) (2 mks)

easySHORT ANSWER4 marks

A pentagon has vertices A(0, 0), B(2, 0), C(2, 2), D(1, 3), and E(0, 2). It is enlarged by a scale factor of 1.5 about the point (1, 1). (a) State the coordinates of the image of vertex A'. (b) Find the coordinates of vertex B' after the enlargement. (c) What are the coordinates of vertex D' after the enlargement? (4 marks)

View Marking Scheme

Part (a) — 1 mark

A' = (1 + 1.5(0 - 1), 1 + 1.5(0 - 1)) = (-0.5, -0.5) (1 mk)

Part (b) — 1 mark

B' = (1 + 1.5(2 - 1), 1 + 1.5(0 - 1)) = (2.5, -0.5) (1 mk)

Part (c) — 2 marks

D' = (1 + 1.5(1 - 1), 1 + 1.5(3 - 1)) = (1, 4) (2 mks)

A rectangle has vertices A(1, 2), B(3, 2), C(3, 4), and D(1, 4). It is enlarged by a scale factor of 2 about the origin. (a) State the new coordinates of vertex A'. (b) What are the coordinates of vertex B' after the enlargement? (c) Find the coordinates of vertex C' after the enlargement. (4 marks)

Geometric transformations (enlargement) — KCSE Mathematics

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Sample Questions

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