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Here is a coordinate grid - OCR - GCSE Maths - Question 5 - 2017 - Paper 1
Question 5
Here is a coordinate grid. (a) Draw the image of triangle A after a reflection in the line $y = 1$. (b) Describe fully the single transformation that maps triangle... show full transcript
Worked Solution & Example Answer:Here is a coordinate grid - OCR - GCSE Maths - Question 5 - 2017 - Paper 1
Step 1
Draw the image of triangle A after a reflection in the line $y = 1$.
Answer
To reflect triangle A over the line , follow these steps:
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Identify the coordinates of the vertices of triangle A:
- Let’s assume triangle A has vertices at coordinates (0, 2), (2, 2), and (2, 4).
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For each vertex, determine its vertical distance from the line :
- For vertex (0, 2), the distance is .
- For vertex (2, 2), the distance is .
- For vertex (2, 4), the distance is .
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Reflect each vertex:
- The new y-coordinate for vertex (0, 2) will be , thus the new vertex is (0, 0).
- The new y-coordinate for vertex (2, 2) will also be , hence the new vertex is (2, 0).
- The new y-coordinate for vertex (2, 4) will be , resulting in (2, 7).
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Connect these new vertices to form the reflected triangle.
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 translation.
- The translation vector can be defined as moving triangle A 3 units to the right and 1 unit up. Therefore, if we denote the translation vector as (3, 1), this explains how each point of triangle A moves to coincide with a corresponding point in triangle B.
Step 3