Year 10 - Coordinate geometry - Free practice
Year 10 Coordinate Geometry Worksheets
Parallel, perpendicular, equations of lines from conditions.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
About this worksheet
Why we built it
Year 10 coordinate geometry adds parallel and perpendicular gradients to the Year 9 toolkit. These worksheets give your student practice writing the equation of a line from varied conditions - the format that shows up on every Year 10 Methods practice test.
What's covered
Sub-skills your student will practise
- ✓Identifying parallel vs perpendicular gradients
- ✓Equation of a line through a point with given gradient
- ✓Equation of a line through two points
- ✓Equation of a line parallel/perpendicular to another
- ✓Distance and midpoint applied to gradient questions
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Frequently asked
Questions parents ask about coordinate geometry
What's special about parallel lines' gradients?
Parallel lines have equal gradients. So if one line has gradient 3, any line parallel to it also has gradient 3. The y-intercepts differ unless they're the same line.
What's special about perpendicular lines' gradients?
Perpendicular gradients multiply to -1. So a line perpendicular to y = 3x + 2 has gradient -1/3. Recognising this saves a lot of working on Year 10 geometry questions.
How do students find the equation of a line from a point and gradient?
Use point-gradient form: y - y1 = m(x - x1). Then rearrange into y = mx + c form. For point (2, 5) and gradient 3: y - 5 = 3(x - 2), so y = 3x - 1.
What does Year 10 coordinate geometry feed into?
Year 11 Methods uses these results constantly in calculus (tangent and normal lines), function transformations, and applications. Year 10 sets up the geometric language Methods relies on.
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