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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 transformati... 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} ), we need to apply the vector to each vertex of triangle T. If the vertices are given as (x, y), the new coordinates after the translation will be:
- New x-coordinate: ( x' = x - 6 )
- New y-coordinate: ( y' = y + 2 )
Thus, if the original vertices of triangle T are (1, 1), (2, 3), and (3, 2), the translated vertices will be:
- (1 - 6, 1 + 2) = (-5, 3)
- (2 - 6, 3 + 2) = (-4, 5)
- (3 - 6, 2 + 2) = (-3, 4)
So the new coordinates after translation are (-5, 3), (-4, 5), and (-3, 4).
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
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Reflection in the line ( y = x ): This transformation swaps the x and y coordinates of any point (x, y) to (y, x).
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Reflection in the x-axis: This transformation changes the sign of the y-coordinate. For a point (y, x), it becomes (y, -x).
Combining these two transformations results in the following:
- Start with a point (x, y)
- After reflecting in the line ( y = x ), the point becomes (y, x)
- After reflecting in the x-axis, the point becomes (y, -x)
Thus, the single transformation equivalent to both is a transformation that takes a point (x, y) directly to (y, -x).