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You may use this coordinate grid to help you answer the following question - OCR - GCSE Maths - Question 11 - 2023 - Paper 4
Question 11
You may use this coordinate grid to help you answer the following question. Describe fully the single transformation that is equivalent to: • a rotation of 180° wi... show full transcript
Worked Solution & Example Answer:You may use this coordinate grid to help you answer the following question - OCR - GCSE Maths - Question 11 - 2023 - Paper 4
Step 1
a rotation of 180° with centre (0, 1)
Answer
To perform a rotation of 180° about the point (0, 1), we use the following transformation formula:
If (x, y) is a point on the coordinate plane, after the rotation the new coordinates (x', y') are given by:
Thus, applying the rotation results in the following transformation:
- The x-coordinate changes to:
- The y-coordinate changes to: .
Step 2
a translation of
Answer
Now, we perform the translation given by the vector (\begin{pmatrix} 4 \ 0 \end{pmatrix}). This means we add 4 to the x-coordinate and 0 to the y-coordinate. Therefore,
The final transformation results in:
We substitute the values from the previous step:
.
Overall, the single transformation can be described as a rotation followed by a translation, resulting in the final coordinates as above.