## sebastiangonzagonza one year ago 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.

1. mathstudent55

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2. mathstudent55

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3. mathstudent55

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

4. sebastiangonzagonza

so i would need three other points?

5. sebastiangonzagonza

its 0,3

6. mathstudent55

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7. mathstudent55

Here is the given point, (0, 3)

8. mathstudent55

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9. sebastiangonzagonza

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

10. mathstudent55

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11. sebastiangonzagonza

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

12. nincompoop

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

13. mathstudent55

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

14. mathstudent55

Arbitrary.

15. sebastiangonzagonza

HAH I dont want to make you fail @mathstudent55

16. sebastiangonzagonza

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

17. mathstudent55

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

18. sebastiangonzagonza

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

19. sebastiangonzagonza

was i correct to do that??

20. mathstudent55

Yes. Good job!

21. nincompoop

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22. nincompoop

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23. mathstudent55

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

24. nincompoop

good job at pointing out the concept, regardless

25. 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

26. sebastiangonzagonza

i believe that i just needed to provide the points.

27. mathstudent55

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28. nincompoop

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

29. mathstudent55

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

30. sebastiangonzagonza

wait what?

31. sebastiangonzagonza

im confused

32. mathstudent55

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33. 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?

34. sebastiangonzagonza

im not sure

35. 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.

36. mathstudent55

Ok so far?

37. sebastiangonzagonza

ohhh okay yes, i understand

38. mathstudent55

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39. 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.

40. mathstudent55

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41. mathstudent55

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

42. mathstudent55

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

43. sebastiangonzagonza

i believe so

44. sebastiangonzagonza

im just a bit slow rn

45. sebastiangonzagonza

its 12:40AM where i am rn

46. mathstudent55

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

47. mathstudent55

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

48. sebastiangonzagonza

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

49. mathstudent55

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

50. sebastiangonzagonza

perfect okay

51. sebastiangonzagonza

lets do it

52. mathstudent55

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53. mathstudent55

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

54. mathstudent55

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55. 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?

56. sebastiangonzagonza

yes

57. 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.

58. sebastiangonzagonza

okay..

59. mathstudent55

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

60. sebastiangonzagonza

so hold on just a second

61. sebastiangonzagonza

how should i write this for the answer?

62. mathstudent55

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63. mathstudent55

I'm doing it now.

64. sebastiangonzagonza

but in words

65. mathstudent55

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

66. mathstudent55

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

67. mathstudent55

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68. mathstudent55

|dw:1439787195206:dw| 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

69. mathstudent55

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70. sebastiangonzagonza

okay

71. mathstudent55

|dw:1439787388301:dw| 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

72. 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.

73. mathstudent55

Since we want to show that angle O and angle Q are supplementary angles, we add their measures. m<O + m<Q = 1/2 x + 180 - 1/2 x m<O + m< Q = 1/2 x - 1/2 x + 180 m<O + m<Q = 180 Since we just showed that the measures of angles O and Q add up to 180 deg, we have proved that the angles are supplementary.

74. mathstudent55

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

75. sebastiangonzagonza

okay

76. sebastiangonzagonza

thank you

77. mathstudent55

yw