Free Grade 3 Distance Between Points in Context Lessons
Free Grade 3 lessons for Distance Between Points in Context: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain distance between points in context
Explain distance between points in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate distance between points in context
Calculate distance between points in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare distance between points in context
Compare distance between points in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify distance between points in context
Justify distance between points in context 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 Distance Between Points in Context 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, 4) in?[1]
- 2.Which quadrant is the point (3, -3) in?[1]
- 3.Which quadrant is the point (-3, 2) in?[1]
- 4.Which quadrant is the point (6, 1) in?[1]
- 5.Find the midpoint of (-6, 4) and (2, 8).[2]
- 6.Find the midpoint of (2, 0) and (12, -4).[2]
- 7.Find the midpoint of (6, -4) and (16, -2).[2]
- 8.Find the midpoint of (-2, 0) and (4, 4).[2]
- 9.Find the equation of the line through (-6, -1) and (2, -1).[3]
- 10.Find the equation of the line through (-1, 6) and (5, 0).[3]
- 11.Find the equation of the line through (-1, -6) and (1, 2).[3]
- 12.Find the equation of the line through (3, 6) and (5, 0).[3]
Show answers and working
1. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
2. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
3. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
4. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
5. (-2, 6)
Average the x values: (-6 + 2) ÷ 2 = -2. Average the y values: (4 + 8) ÷ 2 = 6.
6. (7, -2)
Average the x values: (2 + 12) ÷ 2 = 7. Average the y values: (0 + -4) ÷ 2 = -2.
7. (11, -3)
Average the x values: (6 + 16) ÷ 2 = 11. Average the y values: (-4 + -2) ÷ 2 = -3.
8. (1, 2)
Average the x values: (-2 + 4) ÷ 2 = 1. Average the y values: (0 + 4) ÷ 2 = 2.
9. y = 0x − 1
Gradient m = (-1 − -1) / (2 − -6) = 0. Substitute (-6, -1): c = -1 − 0 × (-6) = -1.
10. y = -1x + 5
Gradient m = (0 − 6) / (5 − -1) = -1. Substitute (-1, 6): c = 6 − -1 × (-1) = 5.
11. y = 4x − 2
Gradient m = (2 − -6) / (1 − -1) = 4. Substitute (-1, -6): c = -6 − 4 × (-1) = -2.
12. y = -3x + 15
Gradient m = (0 − 6) / (5 − 3) = -3. Substitute (3, 6): c = 6 − -3 × 3 = 15.
Worked examples
Which quadrant is the point (1, -2) in?
- x is positive, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Fourth quadrant
Find the midpoint of (-5, 5) and (5, 13).
- Average the x values: (-5 + 5) ÷ 2 = 0.
- Average the y values: (5 + 13) ÷ 2 = 9.
- Answer: (0, 9)
Find the equation of the line through (6, -1) and (14, 1).
- Gradient m = (1 − -1) / (14 − 6) = 0.25.
- Substitute (6, -1): c = -1 − 0.25 × 6 = -2.5.
- Answer: y = 0.25x − 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 Distance Between Points in Context lesson really free?
- Yes. Every lessons 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 Distance Between Points, Introducing Distance Between Points, Midpoints. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Distance Between Points in Context?
- Move on to Plotting Points, Midpoints, which build directly on this idea.
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