About Origin: Challenge & Extension

Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads

About This Worksheet

A worksheet exploring the concept of rotation about the origin by 180°, including procedural, reasoning, and real-world problems to extend understanding.

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Full preview • 11 questions

About Origin: Challenge & Extension

Subject: MathematicsGrade: Grade 8
Name:
Date:
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Untitled Worksheet

Grade Grade 8
A

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.
1.
Plot the point (3, 4) on the grid. Rotate it 180° about the origin. What are the new coordinates?
[2 marks]
2.
Calculate the coordinates of the point (-5, 2) after a 180° rotation about the origin.
[2 marks]
3.
If point (x, y) rotates 180° about the origin and results in (-x, -y), what is the image of the point (7, -3)?
[2 marks]
4.
Construct the point (2, -5), then rotate it 180° about the origin on the grid.
[2 marks]
B

Problem Solving & Reasoning

Answer all questions. Show detailed reasoning and steps.
1.
A triangle has vertices at A(1, 2), B(3, -4), and C(-2, 5). After rotating the triangle 180° about the origin, what are the new coordinates of each vertex? Explain the reasoning.
[4 marks]
2.
A point P is at (x, y). If rotating it 180° about the origin results in the point (-x, -y), what is the original position of P if its image is at (6, -8)?
[3 marks]
C

Real-world Applications

Answer all questions. Use the grid to visualize transformations if needed.
1.
In a game, a character at position (4, -3) is rotated 180° about the origin to find its new position. Where does the character end up? How does understanding this rotation help in planning game movements?
[4 marks]
D

Challenge & Extension

Answer all questions. These are designed to challenge your understanding of rotation about the origin.
1.
Construct a triangle with vertices at (1, 2), (4, 5), and (7, 2). Rotate the entire triangle 180° about the origin. What are the new vertices? Prove your construction.
[4 marks]
2.
A point (x, y) is such that after a 180° rotation about the origin, it coincides with the point (x, y). What are the possible coordinates of such points? Explain.
[3 marks]
E

Mixed Review & Error Analysis

Answer all questions. Review common mistakes and learn from them.
1.
A student claims that rotating (3, -7) 180° about the origin gives (3, -7). Is this correct? Why or why not? Correct the mistake if necessary.
[3 marks]
2.
Common mistake: A student believes that rotating a point (x, y) 180° around the origin results in (x, y). What is the actual image? Explain why.
[2 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet