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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
Answer
To translate triangle T by the vector
,
we will apply the vector translation to each vertex of triangle T. Let’s assume the vertices of triangle T are defined as points A, B, and C. For example, if point A is at (1, 2), we translate it as follows:
New A = (1 - 6, 2 + 2) = (-5, 4)
Similarly, apply this translation to points B and C to determine their new positions.
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
The combined transformation can be understood in two parts:
-
Reflection in the line : This reflection switches the x and y coordinates of each point. If a point is (x, y), it becomes (y, x).
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Reflection in the x-axis: This reflection changes the sign of the y coordinate. A point (y, x) from the first transformation becomes (y, -x).
Thus, the overall transformation can be expressed as:
- Start with a point (x, y).
- After the reflection in the line , it becomes (y, x).
- After the reflection in the x-axis, the final position will be (y, -x).
Therefore, the single transformation equivalent to the two reflections above is: Reflection in the line .