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Produce complete line equations and distinguish parallel, coincident, perpendicular and other intersecting lines · Check your progress
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Produce parallel and perpendicular line equations through a specified point · Check your progress
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Produce a segment midpoint and the complete perpendicular-bisector equation · Check your progress
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Calculate the area enclosed by an explicitly ordered coordinate polygon · Check your progress
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Produce a circle equation, centre and radius from its given algebraic or geometric facts · Check your progress
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Produce a complete tangent equation at a specified point on a single circle · Check your progress
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Produce every real intersection point of one line and one circle · Check your progress
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Produce transformed variables and the complete symbolic straight-line coefficients · Check your progress
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Recover the straight-line equation and original model constants from labelled transformed graphs · Check your progress
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Check again
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Produce complete line equations and distinguish parallel, coincident, perpendicular and other intersecting lines · Check again
After practising what your progress check showed, check those skills again.
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Produce parallel and perpendicular line equations through a specified point · Check again
After practising what your progress check showed, check those skills again.
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Produce a segment midpoint and the complete perpendicular-bisector equation · Check again
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Calculate the area enclosed by an explicitly ordered coordinate polygon · Check again
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Produce a circle equation, centre and radius from its given algebraic or geometric facts · Check again
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Produce a complete tangent equation at a specified point on a single circle · Check again
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Produce every real intersection point of one line and one circle · Check again
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Produce transformed variables and the complete symbolic straight-line coefficients · Check again
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Recover the straight-line equation and original model constants from labelled transformed graphs · Check again
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Retention check
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Produce complete line equations and distinguish parallel, coincident, perpendicular and other intersecting lines · Retention check
Come back later to see whether your learning has lasted.
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Produce parallel and perpendicular line equations through a specified point · Retention check
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Produce a segment midpoint and the complete perpendicular-bisector equation · Retention check
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Calculate the area enclosed by an explicitly ordered coordinate polygon · Retention check
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Produce a circle equation, centre and radius from its given algebraic or geometric facts · Retention check
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Produce a complete tangent equation at a specified point on a single circle · Retention check
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Produce every real intersection point of one line and one circle · Retention check
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Produce transformed variables and the complete symbolic straight-line coefficients · Retention check
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Recover the straight-line equation and original model constants from labelled transformed graphs · Retention check
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Practise: Produce complete line equations and distinguish parallel, coincident, perpendicular and other intersecting lines
Practise questions on the skills you are learning.
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Practise: Produce parallel and perpendicular line equations through a specified point
Practise questions on the skills you are learning.
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Practise: Produce a segment midpoint and the complete perpendicular-bisector equation
Practise questions on the skills you are learning.
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Practise: Calculate the area enclosed by an explicitly ordered coordinate polygon
Practise questions on the skills you are learning.
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Practise: Produce a circle equation, centre and radius from its given algebraic or geometric facts
Practise questions on the skills you are learning.
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Practise: Produce a complete tangent equation at a specified point on a single circle
Practise questions on the skills you are learning.
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Practise: Produce every real intersection point of one line and one circle
Practise questions on the skills you are learning.
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Practise: Produce transformed variables and the complete symbolic straight-line coefficients
Practise questions on the skills you are learning.
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Practise: Recover the straight-line equation and original model constants from labelled transformed graphs
Practise questions on the skills you are learning.
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Next step
Revision notes
Use coordinate geometry for lines and circles, and linearise power and exponential relationships.
Key ideas
- Coordinate circles and perpendicular lines
Use perpendicular directions, midpoint and area conditions, then recover a circle and verify tangency on the original equation.
- Recover a circle and find every intersection
Use equal-distance conditions to recover a circle, then solve and check complete line–circle intersection sets.
- Linearise power and exponential models
Choose transformed axes, recover power or exponential constants and test the model against original data and domain limits.
From the G3 Additional Mathematics 2027 syllabus
- Condition for two lines to be parallel or perpendicular
- Midpoint of line segment
- Area of rectilinear figure
- Coordinate geometry of circles in the form:
- (x − a)² + (y − b)² = r^2
- x^2 + y^2 + 2gx + 2 fy + c = 0 (excluding problems involving two circles)
- Transformation of given relationships, including y = ax^n and y = kb^x, to linear form to determine unknown constants from a straight line graph