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Square ABCD is transformed by a combined transformation of a reflection in the line $x = -1$ followed by a rotation - Edexcel - GCSE Maths - Question 25 - 2019 - Paper 2
Question 25
Square ABCD is transformed by a combined transformation of a reflection in the line $x = -1$ followed by a rotation. Under the combined transformation, two vertices... show full transcript
Worked Solution & Example Answer:Square ABCD is transformed by a combined transformation of a reflection in the line $x = -1$ followed by a rotation - Edexcel - GCSE Maths - Question 25 - 2019 - Paper 2
Step 1
Describe fully one possible rotation.
Answer
One possible rotation that keeps two vertices of square ABCD invariant is a rotation of 180° about the center of the square.
To clarify, let's identify the coordinates of the vertices of square ABCD:
- A (1, 5)
- B (5, 5)
- C (5, 1)
- D (1, 1)
The center of the square, which is the point about which we will rotate, is given by: ext{Center} = igg( rac{x_A + x_C}{2}, rac{y_A + y_C}{2} igg) = igg( rac{1+5}{2}, rac{5+1}{2} igg) = (3, 3)
When rotating 180° about this center, the new positions of the vertices can be determined as follows:
- The point A (1, 5) will move to (5, 1).
- The point B (5, 5) will move to (1, 1).
- The point C (5, 1) will move to (1, 5).
- The point D (1, 1) will move to (5, 5).
In this case, the vertices A (1, 5) and C (5, 1) are invariant under reflection in the line before the rotation. Thus, a rotation of 180° about (3, 3) after the reflection keeps those vertices the same.