Free Grade 3 Introducing Distance Between Points Quizzes
Free Grade 3 quizzes for Introducing Distance Between Points: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing distance between points
Identify introducing distance between points accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing distance between points
Explain introducing distance between points accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing distance between points
Calculate introducing distance between points accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing distance between points
Compare introducing distance between points 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 Introducing Distance Between Points 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, 3) in?[1]
- 2.Which quadrant is the point (-6, 6) in?[1]
- 3.Which quadrant is the point (3, 1) in?[1]
- 4.Which quadrant is the point (3, 3) in?[1]
- 5.Find the midpoint of (-3, -2) and (3, 4).[2]
- 6.Find the midpoint of (-4, -6) and (0, -12).[2]
- 7.Find the midpoint of (2, 0) and (4, 0).[2]
- 8.Find the midpoint of (-4, 2) and (2, -6).[2]
- 9.Find the equation of the line through (6, -6) and (12, -6).[3]
- 10.Find the equation of the line through (4, 1) and (10, -3).[3]
- 11.Find the equation of the line through (3, -3) and (11, -9).[3]
- 12.Find the equation of the line through (-4, 6) and (0, 4).[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. First quadrant
x is positive, 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. (0, 1)
Average the x values: (-3 + 3) ÷ 2 = 0. Average the y values: (-2 + 4) ÷ 2 = 1.
6. (-2, -9)
Average the x values: (-4 + 0) ÷ 2 = -2. Average the y values: (-6 + -12) ÷ 2 = -9.
7. (3, 0)
Average the x values: (2 + 4) ÷ 2 = 3. Average the y values: (0 + 0) ÷ 2 = 0.
8. (-1, -2)
Average the x values: (-4 + 2) ÷ 2 = -1. Average the y values: (2 + -6) ÷ 2 = -2.
9. y = 0x − 6
Gradient m = (-6 − -6) / (12 − 6) = 0. Substitute (6, -6): c = -6 − 0 × 6 = -6.
10. y = -0.67x + 3.67
Gradient m = (-3 − 1) / (10 − 4) = -0.67. Substitute (4, 1): c = 1 − -0.67 × 4 = 3.67.
11. y = -0.75x − 0.75
Gradient m = (-9 − -3) / (11 − 3) = -0.75. Substitute (3, -3): c = -3 − -0.75 × 3 = -0.75.
12. y = -0.5x + 4
Gradient m = (4 − 6) / (0 − -4) = -0.5. Substitute (-4, 6): c = 6 − -0.5 × (-4) = 4.
Worked examples
Which quadrant is the point (4, 3) in?
- x is positive, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: First quadrant
Find the midpoint of (-1, 5) and (9, 5).
- Average the x values: (-1 + 9) ÷ 2 = 4.
- Average the y values: (5 + 5) ÷ 2 = 5.
- Answer: (4, 5)
Find the equation of the line through (4, 5) and (8, 13).
- Gradient m = (13 − 5) / (8 − 4) = 2.
- Substitute (4, 5): c = 5 − 2 × 4 = -3.
- Answer: y = 2x − 3
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 Introducing Distance Between Points 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 Midpoints. 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 Introducing Distance Between Points?
- Move on to Working with Distance Between Points, Distance Between Points in Context, Plotting Points, Midpoints, which build directly on this idea.
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