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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 \( \begin{pmatrix} -1 \ -3 \end{pmatrix} \). Label ... show full transcript
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 need to apply the rotation formula. The coordinates of a point ((x, y)) after a 180° rotation become ((-x, -y)).
Using this formula, if trapezium T has vertices at points:
- A: (2, -1)
- B: (5, -2)
- C: (4, -4)
- D: (1, -3)
We calculate the new coordinates as follows:
- A' = (-2, 1)
- B' = (-5, 2)
- C' = (-4, 4)
- D' = (-1, 3)
The new trapezium is labeled A.
Step 2
Translate trapezium T by the vector \( \begin{pmatrix} -1 \ -3 \end{pmatrix} \)
Answer
To translate trapezium T by the vector ( \begin{pmatrix} -1 \ -3 \end{pmatrix} ), we need to add the vector components to each vertex of trapezium T.
For the vertices of trapezium T:
- A: (2, -1)
- B: (5, -2)
- C: (4, -4)
- D: (1, -3)
We calculate the new vertices after translation:
- A'' = (2-1, -1-3) = (1, -4)
- B'' = (5-1, -2-3) = (4, -5)
- C'' = (4-1, -4-3) = (3, -7)
- D'' = (1-1, -3-3) = (0, -6)
The new trapezium is labeled B.