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### Paper 2

ANALYTICAL GEOMETRY
Use a Cartesian co-ordinate system to derive and apply:
(a) the equation of a line through two given points
(b) the equation of a line through one point and parallel or perpendicular to a given line
(c) the inclination of a line.

Clarification

• Assessment standards from Grade 10 will be assumed knowledge.
• The concept of collinearity must be understood.
• Prove properties of polygons using analytical methods.
For example:
A(–1 ; –2),
B(–4 ; 2),
C(1 ; 2) and
D(4 ; –2)
is a rhombus.

Use a two-dimensional Cartesian co-ordinate system to derive and apply:
(a) the equation of a circle (any centre);
(b) the equation of a tangent to a circle given a point on the circle.

Clarification

• All assessment standards from Grade 10 and 11 will be assumed knowledge.
• Learners are expected to know and be able to use as an axiom:
"The tangent to a circle is perpendicular to the radius drawn to the point of contact."
• Concepts such as:
- Inscribed-centre
- Circumscribed
- Incentre
- Orthocentre
- Centroid
will not be examined.