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Triangle A and triangle B are drawn on the coordinate grid - OCR - GCSE Maths - Question 10 - 2018 - Paper 5
Question 10
Triangle A and triangle B are drawn on the coordinate grid. (a) (i) Draw the image of triangle A after a rotation of 180° about (0, 0). (ii) Draw the image of tria... show full transcript
Worked Solution & Example Answer:Triangle A and triangle B are drawn on the coordinate grid - OCR - GCSE Maths - Question 10 - 2018 - Paper 5
Step 1
(i) Draw the image of triangle A after a rotation of 180° about (0, 0).
Answer
To rotate triangle A by 180° about the origin (0, 0), we need to apply the following transformation to each vertex of the triangle.
For a point ((x, y)), the rotation is given by:
[ (x, y) \rightarrow (-x, -y) ]
If the vertices of triangle A are at points ((x_1, y_1), (x_2, y_2), (x_3, y_3)), then after rotation, they will move to ((-x_1, -y_1), (-x_2, -y_2), (-x_3, -y_3)). The new coordinates of triangle A after this transformation should be accurately plotted on the grid.
Step 2
(ii) Draw the image of triangle A after a translation by the vector \( \begin{pmatrix} 2 \ -7 \end{pmatrix} \).
Answer
To translate triangle A by the vector ( \begin{pmatrix} 2 \ -7 \end{pmatrix} ), we add the vector's components to each vertex of triangle A.
If the vertices of triangle A are ((x_1, y_1), (x_2, y_2), (x_3, y_3)), then their new positions after translation will be:
[ (x_1 + 2, y_1 - 7), (x_2 + 2, y_2 - 7), (x_3 + 2, y_3 - 7) ]
These new coordinates should also be accurately plotted on the grid.
Step 3
(b) Describe fully the single transformation that maps triangle A onto triangle B.
Answer
The single transformation that maps triangle A onto triangle B can be described as an enlargement. To determine the scaling factor and the center of enlargement, we can analyze the coordinates of the corresponding vertices of both triangles.
If triangle A is scaled up or down to reach the position of triangle B, we must identify the center of enlargement and the ratio of the corresponding sides. The transformation can be expressed in the form "Enlargement with center (1, 2) and scale factor (k)" where (k) adjusts the size appropriately to fit triangle B.