Free Grade 3 Working with Parallel and Perpendicular Lines Quizzes
Free Grade 3 quizzes for Working with Parallel and Perpendicular Lines: 12 real questions with a full answer key and worked solutions. A coordinate (x, y) gives a position: across first, then up. The gradient of a line is rise over run, and y = mx + c describes a straight line.
Free
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with parallel and perpendicular lines
Identify working with parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with parallel and perpendicular lines
Explain working with parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with parallel and perpendicular lines
Calculate working with parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with parallel and perpendicular lines
Compare working with parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Parallel and Perpendicular Lines works
A coordinate (x, y) gives a position: across first, then up. The gradient of a line is rise over run, and y = mx + c describes a straight line.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Which quadrant is the point (1, 3) in?[1]
- 2.Which quadrant is the point (-4, 4) in?[1]
- 3.Which quadrant is the point (-1, -5) in?[1]
- 4.Which quadrant is the point (-3, -2) in?[1]
- 5.Find the midpoint of (0, 1) and (8, 9).[2]
- 6.Find the midpoint of (-6, -2) and (2, -6).[2]
- 7.Find the midpoint of (3, 6) and (5, 12).[2]
- 8.Find the midpoint of (-5, -4) and (-1, -6).[2]
- 9.Find the equation of the line through (-3, -2) and (3, -6).[3]
- 10.Find the equation of the line through (-3, 5) and (3, 5).[3]
- 11.Find the equation of the line through (-1, -6) and (1, -12).[3]
- 12.Find the equation of the line through (5, -1) and (7, -1).[3]
Show answers and working
1. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
2. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
3. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
4. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
5. (4, 5)
Average the x values: (0 + 8) ÷ 2 = 4. Average the y values: (1 + 9) ÷ 2 = 5.
6. (-2, -4)
Average the x values: (-6 + 2) ÷ 2 = -2. Average the y values: (-2 + -6) ÷ 2 = -4.
7. (4, 9)
Average the x values: (3 + 5) ÷ 2 = 4. Average the y values: (6 + 12) ÷ 2 = 9.
8. (-3, -5)
Average the x values: (-5 + -1) ÷ 2 = -3. Average the y values: (-4 + -6) ÷ 2 = -5.
9. y = -0.67x − 4
Gradient m = (-6 − -2) / (3 − -3) = -0.67. Substitute (-3, -2): c = -2 − -0.67 × (-3) = -4.
10. y = 0x + 5
Gradient m = (5 − 5) / (3 − -3) = 0. Substitute (-3, 5): c = 5 − 0 × (-3) = 5.
11. y = -3x − 9
Gradient m = (-12 − -6) / (1 − -1) = -3. Substitute (-1, -6): c = -6 − -3 × (-1) = -9.
12. y = 0x − 1
Gradient m = (-1 − -1) / (7 − 5) = 0. Substitute (5, -1): c = -1 − 0 × 5 = -1.
Worked examples
Which quadrant is the point (-3, -6) in?
- x is negative, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Third quadrant
Find the midpoint of (-4, -4) and (2, 4).
- Average the x values: (-4 + 2) ÷ 2 = -1.
- Average the y values: (-4 + 4) ÷ 2 = 0.
- Answer: (-1, 0)
Find the equation of the line through (-3, 1) and (1, 3).
- Gradient m = (3 − 1) / (1 − -3) = 0.5.
- Substitute (-3, 1): c = 1 − 0.5 × (-3) = 2.5.
- Answer: y = 0.5x + 2.5
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Plots (y, x) instead of (x, y).
Correction: Along the corridor, then up the stairs.
Calculates gradient as run over rise.
Correction: Gradient = change in y ÷ change in x.
Teacher tips
- · Play coordinate battleships.
Parent tips
- · Find places on a map using grid references.
Real-life applications
- · Maps, game boards, GPS.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Parallel and Perpendicular Lines quiz really free?
- Yes. Every quizzes on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Introducing Parallel and Perpendicular Lines, y = mx + c. Each one has its own free lesson, worksheet and quiz.
- How is the quiz sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Parallel and Perpendicular Lines?
- Move on to Parallel and Perpendicular Lines in Context, Gradient, y = mx + c, which build directly on this idea.
Related resources
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