Parallel Lines: Challenge & Extension
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring properties of parallel lines through vector geometry, including proofs, problem solving, and real-world applications for Grade 8 students.
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Full preview • 11 questions
Parallel Lines: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Introduction
Review the key concept: Two lines are parallel if their direction vectors are scalar multiples. Recall that if vectors **a** and **b** are parallel, then **a = k * b** for some scalar k.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Given vectors **u = (3, 4)** and **v = (6, 8)**, determine whether the lines defined by these vectors are parallel.
[2 marks]2.
Calculate the scalar multiple **k** such that **u = k * v** for **u = (9, 12)** and **v = (3, 4)**.
[3 marks]3.
Construct a pair of parallel lines passing through points A(2, 3) and B(5, 7). Find the direction vector of these lines.
[3 marks]4.
Prove that if vectors **a** and **b** are parallel, then any vector perpendicular to **a** is also perpendicular to **b**.
[4 marks]5.
A line passing through point (1,2) has direction vector (2, 3). Find the equation of a line parallel to it passing through point (4,5).
[3 marks]6.
In a diagram, two lines are shown with direction vectors (2, -1) and (4, -2). Are these lines parallel? Justify your answer.
[2 marks]7.
Given a pair of parallel lines with a common direction vector **d = (5, -5)**, find a vector perpendicular to **d**.
[2 marks]8.
A transversal cuts two parallel lines. The alternate interior angles are given as 70° and 110°. Explain why these lines are parallel or not.
[4 marks]9.
Determine whether the vectors **a = (1, 2)** and **b = (2, 4)** are parallel. Then, find the equation of the line through (0,0) parallel to **a**.
[3 marks]10.
Challenge: Given two lines with equations y = 3x + 2 and y = 3x - 4, prove they are parallel using vector methods.
[4 marks]11.
Error Analysis: A student claims that if two vectors are not scalar multiples, then the lines are not parallel. Is this correct? Explain.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet