A point A is graphed at (0, 3). Complete the coordinates of a shape that can be rotated about the y-axis to create a cylinder. Provide an explanation for your answer to receive full credit.

- sebastiangonzagonza

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- mathstudent55

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- mathstudent55

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- mathstudent55

If you rotate that rectangle about the y-axis, you get the cylinder in the figure.

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## More answers

- sebastiangonzagonza

so i would need three other points?

- sebastiangonzagonza

its 0,3

- mathstudent55

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- mathstudent55

Here is the given point, (0, 3)

- mathstudent55

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- sebastiangonzagonza

okay so i would i have to use (0,0), (2,3), and (2,0)?

- mathstudent55

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- sebastiangonzagonza

i believe that would make a rectangle and when its rotated, itll become a cylinder

- nincompoop

how did you determine the rest of the dimensions when you were only given one point?

- mathstudent55

Excellent job!
Are you sure you need to ask me questions.
Maybe I should be asking you to help me.

- mathstudent55

Arbitrary.

- sebastiangonzagonza

HAH I dont want to make you fail @mathstudent55

- sebastiangonzagonza

@nincompoop i used 0,3 as a starting point. I then used the other points to create a rectangle.

- mathstudent55

When a rectangle that has an edge on the y-axis rotates about the y-axis, it creates a cylinder.

- sebastiangonzagonza

if you plug that all into geogebra or another graphing thing, you'll be able to see that it forms a rectangle

- sebastiangonzagonza

was i correct to do that??

- mathstudent55

Yes. Good job!

- nincompoop

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- nincompoop

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- mathstudent55

The problem asked for points, not equations.
Also your triangle will yield a cone of rotation, not a cylinder.

- nincompoop

good job at pointing out the concept, regardless

- sebastiangonzagonza

Quadrilateral OPQR is inscribed inside a circle as shown below. Write a proof showing that angles O and Q are supplementary.
Here is the question again

- sebastiangonzagonza

i believe that i just needed to provide the points.

- mathstudent55

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- nincompoop

cylinder is simply a cone, particularly when we are talking about projective geometry

- mathstudent55

@sebastiangonzagonza
What is the arc measure in degrees of a full circle?

- sebastiangonzagonza

wait what?

- sebastiangonzagonza

im confused

- mathstudent55

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- mathstudent55

Look at the figure above.
It shows circle O and a central angle of 80 degrees.
What is x, the arc measure of the arc intercepted by the central angle of 80 degrees?

- sebastiangonzagonza

im not sure

- mathstudent55

Ok, no problem.
The arc measure is the same as the central angle measure.
Since the central angle is 80 deg, then x is also 80 deg.

- mathstudent55

Ok so far?

- sebastiangonzagonza

ohhh okay yes, i understand

- mathstudent55

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- mathstudent55

That was the case of a central angle.
Now we need the case of an inscribed angle.
An inscribed angle is an angle whose vertex is on the circle itself.

- mathstudent55

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- mathstudent55

In the case of an inscribed angle, the measure of the intercepted arc is twice the measure of the inscribed angle.

- mathstudent55

Are you ok with central angle and arc & inscribed angle and arc?

- sebastiangonzagonza

i believe so

- sebastiangonzagonza

im just a bit slow rn

- sebastiangonzagonza

its 12:40AM where i am rn

- mathstudent55

Here's a summary:
central angle measure = arc measure
inscribed angle measure = 1/2 arc measure

- mathstudent55

Ok. I'll just finish this problem and that 'll be it for tonight.

- sebastiangonzagonza

and this is for the Quadrilateral OPQR is inscribed inside a circle question?

- mathstudent55

Yes. Now let's get back to our inscribed quadrilateral.

- sebastiangonzagonza

perfect okay

- sebastiangonzagonza

lets do it

- mathstudent55

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- mathstudent55

Here is the inscribed quadrilateral.
Let's call the circle circle C with center at point C.

- mathstudent55

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- mathstudent55

If you use CA as the side of a central angle, and you go around a full rotation until you end up again at CA, that would be a 360-deg angle, right?

- sebastiangonzagonza

yes

- mathstudent55

Then since that central angle measures 360 degrees, that means that a circle is considered to be an arc of measure 360 deg.
Remember, we saw before that the arc measure is the same as the central angle measure.

- sebastiangonzagonza

okay..

- mathstudent55

Now let's deal with angles O and Q to prove they are supplementary.

- sebastiangonzagonza

so hold on just a second

- sebastiangonzagonza

how should i write this for the answer?

- mathstudent55

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- mathstudent55

I'm doing it now.

- sebastiangonzagonza

but in words

- mathstudent55

The two arcs, x and y, add up to the full circle, so their measures add up to 360 deg.
x + y = 360

- mathstudent55

If we solve for y, we get y = 360 - x
That means we have two arcs of measures x and 360 - x.

- mathstudent55

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- mathstudent55

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Now let's look at angle Q.
Angle Q is an inscribed angle,
An inscribed angle is half of its intercepted arc.
The intercepted arc of angle Q is arc ROP
Since arc ROP has measure x, then the inscribed angle Q has half of that measure, 1/2 x

- mathstudent55

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- sebastiangonzagonza

okay

- mathstudent55

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Now we do the same with angle Q.
Angle Q is an inscribed angle.
Angle Q intercepts arc PQR.
The measure of angle Q is half the measure of angle PQR.
That means the measure of angle Q is 1/2 (360 - x) = 180 - 1/2 x

- mathstudent55

Now that we have measures for angles O and Q, we recall the definition of supplementary angles:
Two angles are supplementary if the sum of their measures is 180 deg.

- mathstudent55

Since we want to show that angle O and angle Q are supplementary angles, we add their measures.
m

- mathstudent55

Ok, gtg, it's very late for me.
If you have any questions, just ask.
I'll try to answer them tomorrow.

- sebastiangonzagonza

okay

- sebastiangonzagonza

thank you

- mathstudent55

yw

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