Swapping & Negating: Real-world Applications in Art & Patterns
Mathematics
Grade 7
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring Swapping & Negating through real-world contexts involving art and pattern design. Students will practice transforming points and shapes using reflection principles.
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Full preview • 13 questions
Swapping & Negating: Real-world Applications in Art & Patterns
Subject: MathematicsGrade: Grade 7
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Untitled Worksheet
Grade Grade 7
A
Introduction
Read the explanation below before attempting the questions.
1.
Swapping the coordinates of a point (x, y) exchanges the positions of x and y. Negating a coordinate changes its sign. When reflecting a point across the line y = -x, the new coordinates are obtained by swapping and negating the original coordinates. For example, the point (3, -4) reflects to (-4, -3).
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Reflect the point (5, -2) across the line y = -x. Write the new coordinates.
[2 marks]2.
Find the reflection of the point (-6, 4) across y = -x.
[2 marks]3.
Plot and reflect the point (2, -3) across y = -x on the grid.
[3 marks]C
Problem Solving & Reasoning
Work through the multi-step problems carefully.
1.
A pattern in an art piece involves points at (x, y). The artist reflects a shape across y = -x. If a point (7, -5) is part of the original pattern, what are its coordinates after reflection? Explain the process.
[4 marks]2.
A design uses points with coordinates (-4, 8), (3, -6), and (0, 0). Reflect these points across y=-x and describe the resulting pattern. How can this reflection enhance the symmetry in the design?
[4 marks]D
Real-world Applications
Answer the following questions based on art and pattern design scenarios.
1.
An artist sketches a pattern with a point at (x, y). To create a symmetrical border, they reflect the pattern across y = -x. If a point is at (3, -7), what are its reflected coordinates? How might this reflection be used to create a mirror image in the art?
[3 marks]2.
A digital pattern uses points at (-2, 5) and (4, -3). If these points are reflected across y = -x, what are their new positions? Describe how such reflections can help in designing seamless tiles for flooring.
[3 marks]E
Challenge & Extension
Attempt these more difficult problems to deepen your understanding.
1.
Design a shape on the grid with points at (x, y). Reflect all points across y = -x. If the original shape has vertices at (2, 3), (-4, 5), and (0, -2), list the reflected vertices and explain the transformation process.
[4 marks]2.
A pattern consists of points at (6, -4), (-3, 7), and (1, -1). Reflect this pattern across y = -x and analyze how the reflection affects the overall symmetry of the pattern. Why is understanding this transformation important in art design?
[4 marks]F
Mixed Review
Solve these questions to review swapping and negating techniques.
1.
Reflect the point (x, y) = (-3, 4) across y = -x. Write the reflected point and verify your answer by checking the process.
[3 marks]2.
Identify and correct the mistake in this reflection process: "To reflect (2, -5), swap to (-5, 2) and then negate to (5, -2)."
[2 marks]G
Error Analysis
Review the common mistake below and explain how to fix it.
1.
A student reflects the point (3, -4) but mistakenly states the result as (4, -3). What is the error, and how should they correctly perform the reflection?
[2 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)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet