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(a) Rotate trapezium T 180° about the origin - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 2
Question 5
(a) Rotate trapezium T 180° about the origin. Label the new trapezium A. (b) Translate trapezium T by the vector (−1, −3). Label the new trapezium B.
Worked Solution & Example Answer:(a) Rotate trapezium T 180° about the origin - Edexcel - GCSE Maths - Question 5 - 2017 - Paper 2
Step 1
Rotate trapezium T 180° about the origin.
Answer
To rotate trapezium T 180° about the origin, we will apply the rotation formula for each point (x, y):
Suppose the vertices of trapezium T are at the points (2, -2), (4, -2), (3, -3), and (1, -3). The new vertices after rotation will be:
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For (2, -2):
- New coordinates = (-2, 2)
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For (4, -2):
- New coordinates = (-4, 2)
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For (3, -3):
- New coordinates = (-3, 3)
-
For (1, -3):
- New coordinates = (-1, 3)
These coordinates will make up the new trapezium A.
Step 2
Translate trapezium T by the vector (−1, −3).
Answer
To translate trapezium T by the vector (-1, -3), we will apply the translation formula to each point (x, y):
Considering the original vertices (2, -2), (4, -2), (3, -3), and (1, -3), the new vertices after translation will be:
-
For (2, -2):
- New coordinates = (2 - 1, -2 - 3) = (1, -5)
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For (4, -2):
- New coordinates = (4 - 1, -2 - 3) = (3, -5)
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For (3, -3):
- New coordinates = (3 - 1, -3 - 3) = (2, -6)
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For (1, -3):
- New coordinates = (1 - 1, -3 - 3) = (0, -6)
These coordinates will represent the new trapezium B.