Swapping Coordinates: Problem Solving & Reasoning
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the concept of swapping coordinates during reflection across the line y=x, with questions ranging from procedural practice to real-world applications and extensions.
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Swapping Coordinates: Problem Solving & Reasoning
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Read the explanation below.
1.
When reflecting a point across the line y = x, the coordinates of the point are swapped. For example, the point (a, b) becomes (b, a).
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Reflect the point (3, 7) across the line y=x. Write the new coordinates.
[2 marks]2.
If a point initially at (−4, 2) is reflected across y=x, what are its new coordinates?
[2 marks]3.
Plot and reflect the point (1, −3) across y=x. What are the resulting coordinates?
[3 marks]4.
Reflect the point (0, 0). What are the new coordinates?
[2 marks]C
Targeted Practice
Answer the following questions, which increase in difficulty.
1.
A triangle has vertices at (2, 5), (4, 7), and (6, 3). Reflect all vertices across y=x. Write down the new vertices.
[4 marks]2.
A point moves from (−1, 4) to its reflection across y=x. Calculate the new coordinates and explain why this transformation works.
[4 marks]3.
Construct a set of points where the x-coordinate is always 3. Reflect them across y=x and describe the change.
[4 marks]4.
Reflect the point (−5, −8) across y=x. Is the point on the same side of the line y=x after reflection? Explain.
[3 marks]D
Challenge & Extension
Tackle these advanced problems involving swapping coordinates.
1.
A quadrilateral has vertices at (1, 2), (4, 5), (6, 2), and (3, 0). Reflect it across y=x and determine the new vertices. Then, describe the shape after reflection.
[5 marks]2.
Given a point (x, y) where x and y are variables, describe the algebraic transformation that results from reflecting across y=x.
[3 marks]E
Mixed Review
Answer these mixed questions on coordinate swapping.
1.
True or False: Reflecting the point (x, y) across y=x always results in a point where the x-coordinate is greater than or equal to the y-coordinate.
[1 mark]2.
Reflect the point (8, -3) across y=x. Then, reflect that point again across y=x. What is the final coordinate?
[3 marks]F
Error Analysis
Identify the mistake and correct it.
1.
A student reflects the point (2, 5) across y=x and incorrectly writes the new point as (2, 5). Why is this wrong, and what should the correct new point be?
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
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- • Add more questions (10 → 15)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet