Show algebraically whether each chord is/is not a dia.....

[hamnet]

Points X(-11,2), Y(-9,4) and Z(5,-10) lie on the circumference of a circle with centre C(-3,-4). Consider chords YZ and XZ. Show algebraically whether each chord is/is not a diameter of the circle.

I am not sure where to begin and what my initial drawing should look like. Can someone help me? :?:

 

[stapel]

You've got the center and points on the "edge". What then is the length of the radius? What then is the length of the diameter?

What are the distances between pairs of points on the "edge"? Does any match the length of the diameter of the circle? If so, is the center point the midpoint between those two "edge" points?

If you get stuck, please reply showing all of your work and reasoning. Thank you.

Eliz.

 

[hamnet]

I am not exactly sure how to use the points given, nor if I am drawing the circle correctly?

 

[stapel]

I am not exactly sure how to use the points given, nor if I am drawing the circle correctly?

Use the points in the manner outlined in my previous reply.

You don't need to draw a circle.

Eliz.

 

[pka]

\(\displaystyle \L \begin{array}{rcl}
D(Y,Z) & = & \sqrt {14^2 + 14^2 } \\
D(X,Z) & = & \sqrt {16^2 + 12^2 } \\
2D(C,X) & = & 2\sqrt {8^2 + 6^2 } \\
\end{array}\)

 

[hamnet]

So I would use some type of formula?

 

[stapel]

So I would use some type of formula?

Yes. Just as another tutor showed, you would find distances by using the Distance Formula; you would find the diameter by doubling the radius; etc.

If you've never heard of the Distance Formula or the Midpoint Formula, and/or aren't familiar with the relationships between centers, radii, and diameters of circles, then it would appear that you have been placed incorrectly.

Please consult with your academic advisor about rectifying this situation.

My best wishes to you.

Eliz.

 

[hamnet]

Thank you. I will have a look at those formulas.

Staple: This is from Grade 12 Math in Canada. It is almost the end of the first semester and our Provincials are coming up soon. Our teacher failed to teach the entire Circle Geometry chapter, otherwise I would know this

 

[pka]

Our teacher failed to teach the entire Circle Geometry chapter, otherwise I would know this

That is Ms Staple's point! You deserve more than that.
So go to the Provincial Education Authority and file a complaint.

 

[hamnet]

I have tried, but it proved to be fruitless :|

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D(Y,Z) = 19.80
D(X,Z) = 20
2D(C,X) = 20

So would this be the answer to the question?