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Triangle A is drawn on the grid below - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

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Question 10

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Triangle A is drawn on the grid below. Enlarge triangle A with scale factor 2 and centre of enlargement (0, 0).

Worked Solution & Example Answer:Triangle A is drawn on the grid below - OCR - GCSE Maths - Question 10 - 2018 - Paper 1

Step 1

Identify the vertices of triangle A

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Answer

The vertices of triangle A on the grid can be identified as follows:

  • A(2, 2)
  • B(4, 2)
  • C(2, 4) These points reference the lower left vertex at (2, 2), the right vertex at (4, 2), and the top vertex at (2, 4).

Step 2

Calculate the enlarged vertices using scale factor 2

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Answer

To enlarge triangle A, we apply the formula for enlargement:

extEnlargedPoint=extScaleFactorimes(extOriginalPoint−extCentreofEnlargement)+extCentreofEnlargement ext{Enlarged Point} = ext{Scale Factor} imes ( ext{Original Point} - ext{Centre of Enlargement}) + ext{Centre of Enlargement}

Using (0, 0) as the centre of enlargement and a scale factor of 2, the calculations are:

  • For A(2, 2):
    • Enlarged A = 2 × (2 - 0, 2 - 0) + (0, 0) = (4, 4)
  • For B(4, 2):
    • Enlarged B = 2 × (4 - 0, 2 - 0) + (0, 0) = (8, 4)
  • For C(2, 4):
    • Enlarged C = 2 × (2 - 0, 4 - 0) + (0, 0) = (4, 8)

Step 3

List the vertices of the enlarged triangle

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Answer

The vertices of the enlarged triangle A are:

  • Enlarged A(4, 4)
  • Enlarged B(8, 4)
  • Enlarged C(4, 8) These points now represent the new positions of triangle A after enlargement.

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