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Triangle A and triangle B are drawn on the coordinate grid - OCR - GCSE Maths - Question 15 - 2017 - Paper 1
Question 15
Triangle A and triangle B are drawn on the coordinate grid. (a) Translate triangle A by vector \( \begin{pmatrix} 3 \\ -5 \end{pmatrix} \). (b) Describe fully the... show full transcript
Worked Solution & Example Answer:Triangle A and triangle B are drawn on the coordinate grid - OCR - GCSE Maths - Question 15 - 2017 - Paper 1
Step 1
Translate triangle A by vector \( \begin{pmatrix} 3 \\ -5 \end{pmatrix} \)
Answer
To translate triangle A by the vector ( \begin{pmatrix} 3 \ -5 \end{pmatrix} ), you will move each vertex of triangle A. For example, if the coordinates of triangle A’s vertices are
- Vertex 1: (x1, y1)
- Vertex 2: (x2, y2)
- Vertex 3: (x3, y3),
you will add 3 to the x-coordinates and subtract 5 from the y-coordinates:
- New Vertex 1: (x1 + 3, y1 - 5)
- New Vertex 2: (x2 + 3, y2 - 5)
- New Vertex 3: (x3 + 3, y3 - 5).
This will give you the new coordinates for the translated triangle A.
Step 2
Describe fully the single transformation that maps triangle A onto triangle B.
Answer
The transformation that maps triangle A onto triangle B is a combination of a translation and a resizing.
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Translation: Triangle A is translated from its original position to align with triangle B. The vector of translation can be determined by finding the difference in coordinates of corresponding vertices between triangles A and B.
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Resizing: In addition to translation, triangle A might be resized (dilated) to match the dimensions of triangle B. This means that the lengths of the sides of triangle A will be multiplied by a certain scale factor to match those of triangle B.
Therefore, the transformation can be fully described as a translation followed by a dilation.