Free Grade 3 Parallel and Perpendicular Lines Flashcards
Free Grade 3 flashcards for 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify parallel and perpendicular lines
Identify parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain parallel and perpendicular lines
Explain parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate parallel and perpendicular lines
Calculate parallel and perpendicular lines accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare parallel and perpendicular lines
Compare 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 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 (-2, -2) in?[1]
- 2.Which quadrant is the point (4, 6) in?[1]
- 3.Which quadrant is the point (2, -6) in?[1]
- 4.Which quadrant is the point (1, -6) in?[1]
- 5.Find the midpoint of (0, -5) and (6, -11).[2]
- 6.Find the midpoint of (6, -5) and (14, -11).[2]
- 7.Find the midpoint of (-2, -1) and (8, -5).[2]
- 8.Find the midpoint of (-2, 0) and (0, -8).[2]
- 9.Find the equation of the line through (-6, 4) and (4, 4).[3]
- 10.Find the equation of the line through (-5, 6) and (5, 4).[3]
- 11.Find the equation of the line through (-1, 5) and (3, 11).[3]
- 12.Find the equation of the line through (5, 5) and (11, 9).[3]
Show answers and working
1. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
2. First quadrant
x is positive, 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. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
5. (3, -8)
Average the x values: (0 + 6) ÷ 2 = 3. Average the y values: (-5 + -11) ÷ 2 = -8.
6. (10, -8)
Average the x values: (6 + 14) ÷ 2 = 10. Average the y values: (-5 + -11) ÷ 2 = -8.
7. (3, -3)
Average the x values: (-2 + 8) ÷ 2 = 3. Average the y values: (-1 + -5) ÷ 2 = -3.
8. (-1, -4)
Average the x values: (-2 + 0) ÷ 2 = -1. Average the y values: (0 + -8) ÷ 2 = -4.
9. y = 0x + 4
Gradient m = (4 − 4) / (4 − -6) = 0. Substitute (-6, 4): c = 4 − 0 × (-6) = 4.
10. y = -0.2x + 5
Gradient m = (4 − 6) / (5 − -5) = -0.2. Substitute (-5, 6): c = 6 − -0.2 × (-5) = 5.
11. y = 1.5x + 6.5
Gradient m = (11 − 5) / (3 − -1) = 1.5. Substitute (-1, 5): c = 5 − 1.5 × (-1) = 6.5.
12. y = 0.67x + 1.67
Gradient m = (9 − 5) / (11 − 5) = 0.67. Substitute (5, 5): c = 5 − 0.67 × 5 = 1.67.
Worked examples
Which quadrant is the point (1, 6) in?
- x is positive, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: First quadrant
Find the midpoint of (-2, -5) and (8, 1).
- Average the x values: (-2 + 8) ÷ 2 = 3.
- Average the y values: (-5 + 1) ÷ 2 = -2.
- Answer: (3, -2)
Find the equation of the line through (6, 6) and (8, 2).
- Gradient m = (2 − 6) / (8 − 6) = -2.
- Substitute (6, 6): c = 6 − -2 × 6 = 18.
- Answer: y = -2x + 18
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 Parallel and Perpendicular Lines flashcards really free?
- Yes. Every flashcards 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 y = mx + c, Gradient, The Coordinate Plane. Each one has its own free lesson, worksheet and quiz.
- How is the flashcards 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 Parallel and Perpendicular Lines?
- Move on to The Coordinate Plane, which build directly on this idea.
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