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Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 12 - 2020 - Paper 1
Question 12
Triangle T is drawn on a coordinate grid. (a) Translate triangle T by vector \( \begin{pmatrix}-6\\2\end{pmatrix} \). (b) Describe fully the single transformation ... show full transcript
Worked Solution & Example Answer:Triangle T is drawn on a coordinate grid - OCR - GCSE Maths - Question 12 - 2020 - Paper 1
Step 1
Translate triangle T by vector \( \begin{pmatrix}-6\\2\end{pmatrix} \)
Answer
To translate triangle T by the vector ( \begin{pmatrix}-6\2\end{pmatrix} ), you need to move each vertex of triangle T. For each vertex ( (x, y) ) of the triangle, you would perform the following calculation:
- New x-coordinate: ( x - 6 )
- New y-coordinate: ( y + 2 )
For example, if a vertex of triangle T is located at ( (2, 1) ), after the translation it will be at ( (2 - 6, 1 + 2) = (-4, 3) ).
Step 2
Describe fully the single transformation that is equivalent to: a reflection in the line \( y = x \), followed by a reflection in the x-axis.
Answer
The transformation can be described in two steps:
-
Reflection in the line ( y = x ):
- This transformation swaps the coordinates of each point. Therefore, any point ( (a, b) ) after this transformation becomes ( (b, a) ).
-
Reflection in the x-axis:
- This changes the sign of the y-coordinate. Therefore, a point ( (b, a) ) becomes ( (b, -a) ).
Consequently, when combining these transformations, a point originally at ( (x, y) ) will first become ( (y, x) ) after reflecting in the line ( y = x ) and then transform to ( (y, -x) ) after reflecting in the x-axis.