Learning Resources

Outcomes

In this lesson you will

• Examine the slopes of parallel and perpendicular lines using coordinate geometry.

By the end of this section you should be able to:

• Apply inductive reasoning to make conjectures in geometric situations.
• Develop and apply formulas for distance and midpoint.
• Investigate, and make and prove conjectures associated with chord properties of circles.
• Write proofs using various axiomatic systems and assess the validity of deductive arguments.
• Apply properties of circles.
• Solve problems involving the equations and characteristics of circles and ellipses.

Introduction

In this section you will develop theory associated with coordinate geometry while the discussion of the sports and activity complex construction is continued.

You will investigate and discuss the slopes of parallel and perpendicular lines as you examine the placement of walkways and bus shelters, and the location of the queue lines for ticket buyers.

The location of washrooms within the arena is the context for the development of the distance formula for horizontal, vertical, and oblique distances between two points. The location of the concession stand creates the need for the development of the midpoint formula.

You will check the chord properties learned in the previous section using coordinate geometry.

This section should take you between 4 and 5 hours to complete.

Prerequisites

To be successful in this lesson, it would be helpful to know the following:

• Definition of parallel and perpendicular lines.
• Definition of parallelogram, square, right triangle.
• How to set up a set of axes and plot points in a Cartesian plane.
• The formula for the slope of a line given two points on the line.