The diagram shows triangle A drawn on a grid. Kyle reflects triangle A in the x-axis to get triangle B. He then reflects triangle B in the line 𝑦 = 𝑥 to get triangle C. Amy reflects triangle A in the line 𝑦 = 𝑥 to get triangle D. She is then going to reflect triangle D in the x-axis to get triangle E. Is Amy correct? You must show how you get your answer. (Total for Question 9 is 3 marks)

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The diagram shows triangle A drawn on a grid - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2

Question 9

The diagram shows triangle A drawn on a grid. Kyle reflects triangle A in the x-axis to get triangle B. He then reflects triangle B in the line 𝑦 = 𝑥 to get trian... show full transcript

Worked Solution & Example Answer:The diagram shows triangle A drawn on a grid - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2

Step 1

Kyle reflects triangle A in the x-axis to get triangle B.

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Answer

To perform this reflection, each point of triangle A will have its y-coordinate negated. For instance, if point A is at (x, y), then reflection in the x-axis results in point B at (x, -y).

Step 2

He then reflects triangle B in the line 𝑦 = 𝑥 to get triangle C.

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Answer

For the reflection in the line 𝑦 = 𝑥, we swap the x and y coordinates of each vertex of triangle B. Thus, if triangle B has a vertex at (x, -y), it will move to (-y, x). The result will be triangle C.

Step 3

Is Amy correct?

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Answer

Amy first reflects triangle A in the line 𝑦 = 𝑥, which generates a triangle D at the positions where the vertices of A are swapped. Next, when she reflects triangle D in the x-axis, it will result in triangle E; however, triangle E will not be in the same position as triangle C as they follow different transformations. Therefore, Amy is not correct.

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The diagram shows triangle A drawn on a grid - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2

Worked Solution & Example Answer:The diagram shows triangle A drawn on a grid - Edexcel - GCSE Maths - Question 9 - 2017 - Paper 2

Kyle reflects triangle A in the x-axis to get triangle B.

He then reflects triangle B in the line 𝑦 = 𝑥 to get triangle C.

Is Amy correct?

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