Free Grade 3 Working with Parallel and Perpendicular Lines Word Problems Quizzes
Free Grade 3 quizzes for Working with Parallel and Perpendicular Lines Word Problems: 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.
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Stretch
30 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 word problems
Identify working with parallel and perpendicular lines word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with parallel and perpendicular lines word problems
Explain working with parallel and perpendicular lines word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with parallel and perpendicular lines word problems
Calculate working with parallel and perpendicular lines word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with parallel and perpendicular lines word problems
Compare working with parallel and perpendicular lines word problems 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 Word Problems 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 (-6, -1) in?[1]
- 2.Which quadrant is the point (-4, 5) in?[1]
- 3.Which quadrant is the point (1, -3) in?[1]
- 4.Which quadrant is the point (-5, -5) in?[1]
- 5.Find the midpoint of (-2, 3) and (0, 9).[2]
- 6.Find the midpoint of (-1, 2) and (3, 2).[2]
- 7.Find the midpoint of (-6, 0) and (0, 0).[2]
- 8.Find the midpoint of (-4, -1) and (6, 7).[2]
- 9.Find the equation of the line through (-1, 6) and (1, 14).[3]
- 10.Find the equation of the line through (-4, -3) and (6, -5).[3]
- 11.Find the equation of the line through (-5, -1) and (-1, -9).[3]
- 12.Find the equation of the line through (3, -6) and (13, -12).[3]
Show answers and working
1. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
2. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
3. Fourth quadrant
x is positive, 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. (-1, 6)
Average the x values: (-2 + 0) ÷ 2 = -1. Average the y values: (3 + 9) ÷ 2 = 6.
6. (1, 2)
Average the x values: (-1 + 3) ÷ 2 = 1. Average the y values: (2 + 2) ÷ 2 = 2.
7. (-3, 0)
Average the x values: (-6 + 0) ÷ 2 = -3. Average the y values: (0 + 0) ÷ 2 = 0.
8. (1, 3)
Average the x values: (-4 + 6) ÷ 2 = 1. Average the y values: (-1 + 7) ÷ 2 = 3.
9. y = 4x + 10
Gradient m = (14 − 6) / (1 − -1) = 4. Substitute (-1, 6): c = 6 − 4 × (-1) = 10.
10. y = -0.2x − 3.8
Gradient m = (-5 − -3) / (6 − -4) = -0.2. Substitute (-4, -3): c = -3 − -0.2 × (-4) = -3.8.
11. y = -2x − 11
Gradient m = (-9 − -1) / (-1 − -5) = -2. Substitute (-5, -1): c = -1 − -2 × (-5) = -11.
12. y = -0.6x − 4.2
Gradient m = (-12 − -6) / (13 − 3) = -0.6. Substitute (3, -6): c = -6 − -0.6 × 3 = -4.2.
Worked examples
Which quadrant is the point (-1, 5) in?
- x is negative, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: Second quadrant
Find the midpoint of (4, -3) and (10, 5).
- Average the x values: (4 + 10) ÷ 2 = 7.
- Average the y values: (-3 + 5) ÷ 2 = 1.
- Answer: (7, 1)
Find the equation of the line through (-3, -6) and (5, -10).
- Gradient m = (-10 − -6) / (5 − -3) = -0.5.
- Substitute (-3, -6): c = -6 − -0.5 × (-3) = -7.5.
- Answer: y = -0.5x − 7.5
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 Word Problems 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 Working with Parallel and Perpendicular Lines Techniques, Working with Parallel and Perpendicular Lines Essentials, Introducing Parallel and Perpendicular Lines. 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 Word Problems?
- Move on to Working with Parallel and Perpendicular Lines Common Errors, Introducing Parallel and Perpendicular Lines, Parallel and Perpendicular Lines in Context, which build directly on this idea.
Related resources
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