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Enlarge shape P by scale factor \( \frac{1}{2} \) with centre of enlargement (0, 0) - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 1

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Question 18

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Enlarge shape P by scale factor \( \frac{1}{2} \) with centre of enlargement (0, 0). Label your image Q.

Worked Solution & Example Answer:Enlarge shape P by scale factor \( \frac{1}{2} \) with centre of enlargement (0, 0) - Edexcel - GCSE Maths - Question 18 - 2017 - Paper 1

Step 1

Find the coordinates of shape P

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Answer

Identify the vertices of shape P. Assume the vertices of shape P are A(2, 3), B(2, 7), and C(5, 3).

Step 2

Calculate the new coordinates after enlargement

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Answer

Using the scale factor ( k = \frac{1}{2} ) and the centre of enlargement (0, 0), apply the formula for enlargement:

New coordinates = (Original coordinates) × Scale factor.

  • A' = (2 × ( \frac{1}{2} ), 3 × ( \frac{1}{2} )) = (1, 1.5)
  • B' = (2 × ( \frac{1}{2} ), 7 × ( \frac{1}{2} )) = (1, 3.5)
  • C' = (5 × ( \frac{1}{2} ), 3 × ( \frac{1}{2} )) = (2.5, 1.5)

Step 3

Label the new image as Q

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Answer

After calculating the new coordinates, label the enlarged shape as Q with the vertices A'(1, 1.5), B'(1, 3.5), and C'(2.5, 1.5).

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