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Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Question 11
Triangle T is drawn on a coordinate grid. (a) Translate triangle T using the vector \( \begin{pmatrix} -3 \\ 1 \end{pmatrix} \). (b) Describe fully the single tra... show full transcript
Worked Solution & Example Answer:Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 11 - 2017 - Paper 1
Step 1
Translate triangle T using the vector \( \begin{pmatrix} -3 \\ 1 \end{pmatrix} \)
Answer
To translate triangle T using the vector ( \begin{pmatrix} -3 \ 1 \end{pmatrix} ), each point of triangle T is adjusted by subtracting 3 from the x-coordinate and adding 1 to the y-coordinate. Thus, if point ( (x, y) ) is a vertex of triangle T, after translation, the new coordinates will be ( (x - 3, y + 1) ).
Step 2
Describe fully the single transformation that represents the following. (i) A rotation with centre (0, 0) of 180° followed by a rotation with centre (0, 0) of 90° clockwise.
Answer
The combined transformation can be described as a rotation of 90° anti-clockwise about the origin. This is because a 180° rotation followed by a 90° clockwise rotation results in an overall movement that is equivalent to a 90° anti-clockwise rotation.
Step 3
Describe fully the single transformation that represents the following. (ii) A reflection in the x-axis followed by a reflection in the y-axis.
Answer
The single transformation resulting from a reflection in the x-axis followed by a reflection in the y-axis is equivalent to a rotation of 180° about the origin. This is because reflecting a point in both axes will return it to a position directly opposite its initial point across the origin.