# Theory

The Inverse Pythagorean Theorem - Yr 7+, not part of curriculum. Knowledge of Pythagoras' theorem, area of a triangle, solving equations.

Perpendicularity - Yr 11+, proof and brief examples.

# Questions

Intercepts puzzle - Yr 8+. Knowledge of equation of a line, definition of intercept, factors.

Shark fin puzzle - Yr 9+. Knowledge of area of a circle. Doesn't require coordinate geometry beyond interpreting the meaning of a graph.

Circles within circles - Yr 9+. Knowledge of Pythagoras/distance formula, area of circle, familiary with coordinate plane.

Various basic questions on graphing lines - Yr 9+. Knowledge of the equation of a line, the definition of intercepts, ability to solve equations.

Probability - Yr 9+. Probability that a point falls within a certain part of the coordinate plane.

Areas, Pythagoras and optional Inverse Pythagoras - Yr 9+. Knowledge of intercepts, Pythagoras, area of a triangle.

Intersection of circles in coordinate plane - Yr 10+. Representing circles using coordinate geometry, area of a circle.

Unexpected use of coordinate geometry - Yr 11+ (technical skills - yr 9 level, but a lot of work so higher level of mathematical maturity required).

Coordinate geometry, perpendicular - Yr 11+. Knowledge of condition on gradients required for perpendicularity, simultaneous equations, quadratic equations.

Coordinate geometry approach to triangle area - Yr 11+. Knowledge of condition for perpendicularity of lines.

An x-intercept problem: trigonometric approach - Yr 11+. Knowledge of tan function in relation to line gradient.

Rotation in the plane - Yr 11+. Trig, rotation of a point about the origin.