Coordinate geometry
Use coordinate geometry for lines and circles, and linearise power and exponential relationships.
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Before you begin
Use coordinate geometry for lines and circles, and linearise power and exponential relationships.
Learning goals
- Reason and calculate using coordinate geometry
Syllabus statements covered
- 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
- 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
Lessons
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- Coordinate circles and perpendicular linesUse perpendicular directions, midpoint and area conditions, then recover a circle and verify tangency on the original equation.
- Linearise power and exponential modelsChoose transformed axes, recover power or exponential constants and test the model against original data and domain limits.