Learning Resources

Lesson

In this lesson there are no new concepts. You will simply combine the work you did on circles and chords with the work you did on coordinated geometry. The work is a straightforward application of the distance, mid-point and slope formulas to various examples dealing with chords in a circle.

To help you with this work, an example is given below.

Example 1:

A circle has centre at the origin and a radius of . Are the points A(6 , 3) and B(-3 , 6) inside, on, or outside the circle? If they are on the circle, show that the segment from the centre to the mid-point of AB is perpendicular to AB.

Solution

After you have viewed the solution, continue reading below for a summary of how to do proofs using coordinate geometry.

1. To prove segments are congruent calculate their length using the distance formula and show that they are equal.
2. To prove segments bisect each other show that they have the same mid-point.
3. To prove segments parallel show that they have the same slope.
4. To prove segments perpendicular show that their slopes are negative reciprocals of each other.

You should now be able to the the exercises in the text associated with this lesson.

Activity

1. Read through example 8 on page 229 & 230 of your text.
2. Complete Focus Question 28 on page 230.
3. Do the CYU Questions 29 - 32, 34, 35 on pages 230 & 231.

When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.

Test Yourself

A circle with centre E(-5 , 3) passes through points F(3 , 9) and G(-5 , 13).

1. What is the length of the radius of the circle?
2. What is the distance from the centre to FG?

Solution