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0580/33 Oct/Nov 2023, Question 6: Describing Transformations

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

Use a quadrilateral diagram with an extended side and a grid of triangles to give angle reasons, name a shape, find y, and describe or perform transformations.

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

Part (ai) · 1 mark

State the geometrical reason that lines PQ and SR are parallel, using the 114° angles.

  1. 1Angle TSR = angle SPQ = 114°
  2. 2These are corresponding angles, and they are equal, so PQ is parallel to SR

AnswerTSR and SPQ (or TPQ) are corresponding angles

Part (aii) · 1 mark

Write the mathematical name of shape PQRS.

  1. 1One pair of parallel sides: PQRS is a trapezium

AnswerTrapezium

Part (aiii) · 2 marks

Use the angle facts to find the value of y.

  1. 1Angle PSR = 180 − 114 = 66°
  2. 2Co-interior angles: y + 3y = 180 (or 114 + 66 + 3y + y = 360)
  3. 34y = 180, y = 45

Answer45

Part (bi) · 3 marks

Describe fully the single transformation mapping triangle A onto triangle B.

  1. 1A(2, −2) → (−2, −2), A(2, −3) → (−3, −2), A(5, −3) → (−3, −5): (x, y) → (y, −x)
  2. 2Rotation, 90° clockwise, centre (0, 0)

AnswerRotation, 90° clockwise, centre (0, 0)

Part (bii) · 2 marks

Describe fully the single transformation mapping triangle A onto triangle C.

  1. 1(2, −2) → (5, 6): move 3 right and 8 up
  2. 2Translation by column vector (3, 8)

AnswerTranslation, column vector (3, 8)

Part (biii) · 2 marks

Enlarge triangle A by scale factor 3 with centre (4, −5) on the grid.

  1. 1From centre (4, −5), multiply each vector to a vertex by 3
  2. 2(2, −2): (−2, 3) × 3 = (−6, 9) → (−2, 4)
  3. 3(2, −3): (−2, 2) × 3 = (−6, 6) → (−2, 1); (5, −3): (1, 2) × 3 = (3, 6) → (7, 1)
  4. 4Draw the triangle at (−2, 1), (7, 1), (−2, 4)

AnswerTriangle at (−2, 1), (7, 1), (−2, 4)

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Also searched as: 0580/33/O/N/23 · 0580_w23_qp_33 · 0580 w23 33 · question 6.
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