This document provides an introduction to analytical geometry for grade 11 students, focusing on concepts such as the distance between points, midpoints, gradients, and the inclination of lines. It revises key grade 10 topics and introduces equations of straight lines along with applications involving quadrilaterals. The chapter includes examples and scenarios that illustrate how to calculate angles and relationships between lines.

1. ANALYTICAL GEOMETRY
GRADE 11

2. Introduction
Analytical Geometry deals with the study of geometry using the
Cartesian Plane. It is an algebraic approach to the study of geometry.

3. Introduction
In this chapter we will deal with:
• Revision of Grade 10 concepts (distance between two points;
midpoint of a line segment; gradient of a line between two points)
• Inclination of a line
• Equation of a straight line
• Applications involving quadrilateral

4. Grade 10 Revision
In Grade 10 the formulae for the distance between two points, the
midpoint of a line segment and the gradient of a line were established.
We will now revise these formulae and their use. Please note that
these formulae can also be used to determine the coordinates of
points.

5. Grade 10 Revision
1. Distance Between Two Points

6. Grade 10 Revision
2. Midpoint of a Line Segment

7. Grade 10 Revision
3. Gradient of a Line

11. Example 1

12. Example 2

14. The Inclination of a Line
04 MAY 2022

15. Introduction
The inclination of a line is the angle formed with the horizontal in an
anti-clockwise direction.
On the Cartesian plane, the inclination of a line is calculated by finding
the angle formed at the x-axis measured in anti-clockwise direction.
θ is the angle of inclination of line AB.

16. Formula for finding the angle of inclination of
a line

17. Two possible scenarios
1. Positive Gradient 2. Negative Gradient

18. Example 1
Determine the inclination of the line segment in each case.

20. Example 2: Inclination between two lines

21. Example 2: Inclination between two lines

23. The Equation of a Straight
Line
06 MAY 2022

24. INTRODUCTION

25. Example1

27. Example 2: parallel and perpendicular lines

29. Example 3: intersecting lines

31. APPLICATION TO QUADRILATERALS

32. APPLICATION TO QUADRILATERALS

33. APPLICATION TO QUADRILATERALS

34. Example 1

35. Example 1

36. Example 2