course Mth 151 _Fxassignment #007
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08:08:01 `q001. Note that there are 7 questions in this assignment. Sketch three points A, B and C forming an equilateral triangle on a piece of paper, with point A at the lower left-hand corner, point B at the lower right-hand corner and point C at the top. Sketch the segments AB and AC. Now double the lengths of AB and AC, and place a point at each of the endpoints of these segments. Connect these new endpoints to form a new equilateral triangle. Two sides of this triangle will have three points marked while the new side will only have its two endpoints marked. Fix that by marking that middle point, so all three sides of your new triangle are marked the same. How many marked points were there in the original triangle, and how many are there in the new triangle?
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RESPONSE --> There are 3 marked points in the old triangle and 6 marked points. The original triangle would have 3 becuase a triangle has three and then when you extend the points it adds three more points. confidence assessment: 3
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08:08:49 The original triangle had the three points A, B and C. When you extended the two sides you marked the new endpoints, then you marked the point in the middle of the third side. So you've got 6 points marked. Click on 'Next Picture' to see the construction. The original points A, B and C are shown in red. The line segments from A to B and from A to C have been extended in green and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and an equally spaced point has been constructed at the midpoint of that side. Your figure should contain the three original points, plus the three points added when the new side was completed.
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RESPONSE --> The original would have three and the extension adds three more. self critique assessment: 3
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08:20:52 `q002. Extend the two sides that meet at A by distances equal to the distance original lengths AC and AB and mark the endpoints of the newly extended segments. Each of the newly extended sides will have 4 marked points. Now connect the new endpoints to form a new right triangle. Mark points along the new side at the same intervals that occur on the other two sides. How many marked points are on your new triangle, and how many in the whole figure?
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RESPONSE --> There are 4 new marks on the new triangle and the whole figure would have 10. confidence assessment: 3
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08:21:32 You added the two new endpoints when you extended the sides. You then should have marked two new points on the new third side, so that each side contains 4 points including its endpoints. Your figure will now contain 10 marked points.
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RESPONSE --> You already have 6 points and you add the new 4 points and would end up with 10 points total. self critique assessment: 3
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08:22:36 `q003. Continue the process for another step-extend each side by a distance equal to the original point-to-point distance. How many points do you have in the new triangle?
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RESPONSE --> The new triangle would contain 5 new points for a total of 15 points in the whole triangle. confidence assessment: 3
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08:24:04 You will add an endpoint to each newly extended side, so each of the new sides will contain 5 points. You will then have to add 3 equally spaced points to the new side, giving you a total of 13 points on the new triangle. In addition there are two marked points inside the triangle, for a total of 15 points. Click on 'Next Picture' to see the construction. The line segments along two sides of the triangle have again been extended and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and equally spaced points have been constructed along that side.
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RESPONSE --> As you entend the triangle you add the new points on lines to the preceding triangle. self critique assessment: 3
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08:25:00 `q004. Continue the process for one more step. How many points do you have in the new triangle?
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RESPONSE --> You would have 6 new points for a total of 22 points total in the triangle. confidence assessment: 3
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08:25:46 You will add an endpoint to each newly extended side, so each of the new sides will contain 6 points. You will then have to add 4 equally spaced points to the new side, giving you a total of 15 points on the new triangle. There are also 5 marked points inside the triangle for a total of 21 marked points.
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RESPONSE --> As you entend your points you add 1 more point to each extension. self critique assessment: 3
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08:28:13 `q005. The sequence of marked points is 3, 6, 10, 15, 21. What do expect will be the next number in this sequence?
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RESPONSE --> 28. 3/6 a difference of 3; 6/10 a difference of 4; 10/15 for a difference of 5; 15/21 for a difference of 6 so you would add 7 to 21 to get 28. confidence assessment: 3
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08:28:46 The differences between these numbers are 3, 4, 5, 6. The next difference, according to this pattern, should be 7, which would make the next number 28.
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RESPONSE --> You would continue with the pattern of 3, 4, 5, 6 and then 7. self critique assessment: 3
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08:30:54 `q006. How can you tell, in terms of the process you used to construct these triangles, that the next number should be 7 greater?
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RESPONSE --> Becuase as you add a new line of points, you add one to the previous number of points on the previous line. confidence assessment: 3
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08:31:25 When you extend the triangle again, you will add two new endpoints and each side will now have 7 points. The 7 points on the new triangle will be all of the new points.
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RESPONSE --> You keep adding one additional point. self critique assessment: 3
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08:33:15 `q007. How do you know this sequence will continue in this manner?
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RESPONSE --> Becuase as you draw the extension you are adding the previous line plus one more point. confidence assessment: 3
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08:33:45 Each time you extend the triangle, each side increases by 1. All the new marked points are on the new side, so the total number of marked points will increase by 1 more than with the previous extension.
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RESPONSE --> Keep adding one point more to your extensions. self critique assessment: 3
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