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Triangle A is transformed by the combined transformation of a rotation of 180° about the point (-2, 0) followed by a translation with vector \( \begin{pmatrix} -3 \\ 2 \end{pmatrix} \) - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 3
Question 1
Triangle A is transformed by the combined transformation of a rotation of 180° about the point (-2, 0) followed by a translation with vector \( \begin{pmatrix} -3 \\... show full transcript
Worked Solution & Example Answer:Triangle A is transformed by the combined transformation of a rotation of 180° about the point (-2, 0) followed by a translation with vector \( \begin{pmatrix} -3 \\ 2 \end{pmatrix} \) - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 3
Step 1
Rotation of 180° about the point (-2, 0)
Answer
To rotate a point ( P(x, y) ) about the point ( O(-2, 0) ) by 180°, we can use the formula:
- Compute the coordinates relative to the origin: [ x' = x + 2, \quad y' = y - 0 ]
- After rotation, the new coordinates will be: [ (x'', y'') = (-x', -y') ]
- Finally, translate the coordinates back: [ x'' + (-2), y'' + 0 ] You will apply that to each vertex of triangle A.
Step 2
Translation by vector ( -3, 2)
Answer
Next, apply the translation vector ( \begin{pmatrix} -3 \ 2 \end{pmatrix} ) to the coordinates obtained after rotation:
[ (x_t, y_t) = (x'' - 3, y'' + 2) ] Verify that the coordinates of triangle A that are invariant under this transformation remain unchanged after applying both transformations.
Step 3