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0580/42 Oct/Nov 2023, Question 1: Translation

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

On a grid, triangle T has vertices (2, 2), (6, 2) and (6, 4). Carry out a translation, reflection, rotation and enlargement of T, and describe transformations linking the images back to T.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Shift triangle T by the vector (−7, 1) and label the resulting triangle K.

  1. 1Move each vertex 7 left and 1 up
  2. 2(2, 2) → (−5, 3), (6, 2) → (−1, 3), (6, 4) → (−1, 5); label it K

AnswerImage at (−5, 3), (−1, 3), (−1, 5)

Part (aii) · 1 mark

Give the single transformation taking triangle K, with vertices (−5, 3), (−1, 3) and (−1, 5), onto triangle T.

  1. 1Translation by column vector (7, −1)

AnswerTranslation, column vector (7, −1)

Part (b) · 2 marks

Mirror triangle T in the horizontal line y = 4.

  1. 1Reflect in y = 4: y → 8 − y
  2. 2(2, 2) → (2, 6), (6, 2) → (6, 6), (6, 4) stays at (6, 4)

AnswerImage at (6, 4), (6, 6), (2, 6)

Part (c) · 2 marks

Turn triangle T 90° clockwise around the origin (0, 0).

  1. 190° clockwise about (0, 0): (x, y) → (y, −x)
  2. 2(2, 2) → (2, −2), (6, 2) → (2, −6), (6, 4) → (4, −6)

AnswerImage at (2, −2), (2, −6), (4, −6)

Part (di) · 2 marks

Scale triangle T about (0, 0) using scale factor −1/2 and label the image P.

  1. 1Multiply each coordinate by −1/2
  2. 2(2, 2) → (−1, −1), (6, 2) → (−3, −1), (6, 4) → (−3, −2); label it P

AnswerImage at (−1, −1), (−3, −1), (−3, −2)

Part (dii) · 2 marks

State the single transformation that carries triangle P onto triangle T.

  1. 1P to T reverses scale factor −1/2: 1 ÷ (−1/2) = −2
  2. 2Enlargement, centre (0, 0), scale factor −2

AnswerEnlargement, centre (0, 0), scale factor −2

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Also searched as: 0580/42/O/N/23 · 0580_w23_qp_42 · 0580 w23 42 · question 1.
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