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TommyTrojan Group Title

Nick plotted A(2, 2), B(3, 4), and C(4, 2) and joined the points to form triangle ABC. He plotted two other points at P(-3, 4) and Q(-2, 2). What should be the coordinates of the third point R to form triangle PQR that is congruent to triangle ABC? (-1, 4) (-2, -5) (-5, 2) (-4, 1)

  • one year ago
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  1. TommyTrojan Group Title
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    @KonradZuse @AccessDenied

    • one year ago
  2. AccessDenied Group Title
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    Have you tried plotting the points that you were given?

    • one year ago
  3. TommyTrojan Group Title
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    Yes, but I still don't get it

    • one year ago
  4. AccessDenied Group Title
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    Could you post that graph here? :)

    • one year ago
  5. TommyTrojan Group Title
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    I actually wrote it on loose leaf paper lol. Soz

    • one year ago
  6. TommyTrojan Group Title
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    But how would you do it?

    • one year ago
  7. AccessDenied Group Title
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    My first step is graphing the points. Then, I'd look for any obvious solutions like if there were symmetries between the points...

    • one year ago
  8. TommyTrojan Group Title
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    OK can I ask you a few more?

    • one year ago
  9. TommyTrojan Group Title
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    Its either a or b

    • one year ago
  10. AccessDenied Group Title
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    Oh, I just realised something -- the points have to correspond for the congruence! It's been a bit since I've done Geometry... lol. :P Let me graph it myself quick.

    • one year ago
  11. TommyTrojan Group Title
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    OK thank you lol no problem

    • one year ago
  12. AccessDenied Group Title
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    PQ = AB QR = BC PR = AC

    • one year ago
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  13. TommyTrojan Group Title
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    So it is either a or b

    • one year ago
  14. AccessDenied Group Title
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    We could either do something like guess and check each point to see if it is the same, or maybe use some algebra and find the point which is a distance of BC from Q and a distance of AC from P

    • one year ago
  15. TommyTrojan Group Title
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    I got a. Is that right?

    • one year ago
  16. AccessDenied Group Title
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    A) appears correct to me as well. :) For Geometry, if it weren't so obvious, we could use distance formula for some arbitrary point R(x,y) that meets those two distance conditions and solve that two-variable system. This one is pretty simple to "see" though.

    • one year ago
  17. TommyTrojan Group Title
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    I have a few more questions, if that's all right with you?

    • one year ago
  18. AccessDenied Group Title
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    I think we'd get two solutions, one would be some sort of fraction or rational and (-1,4) also.

    • one year ago
  19. AccessDenied Group Title
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    Sure, that's fine. :)

    • one year ago
  20. TommyTrojan Group Title
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    OK thank you so much Triangle PQR is similar to triangle ABC in the figure below. What is the perimeter of triangle ABC? 10.5 inches 39.9 inches 42.0 inches 60.65 inches

    • one year ago
  21. TommyTrojan Group Title
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    • one year ago
  22. TommyTrojan Group Title
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    I got B, just checking my work.

    • one year ago
  23. TommyTrojan Group Title
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    @AccessDenied

    • one year ago
  24. AccessDenied Group Title
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    How did you get B)?

    • one year ago
  25. TommyTrojan Group Title
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    Tell you the truth, I guessed, i'm confused on how to do it.

    • one year ago
  26. AccessDenied Group Title
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    Ah, okay. Well, we'd like to first find that one side length that we don't know on the triangle. Ratios of corresponding sides on similar triangles have to be the same, so this is one way to approach it. Set up this proportion of the sides: \( \displaystyle \frac{\text{AC}}{\text{PR}} = \frac{\text{AB}}{\text{PQ}} \) Notice how these are in fact corresponding sides; we can tell by which angles they are between, or just by position in the name of the triangles. \( \color{green}{\textbf{A}}\text{B}\color{green}{\textbf{C}} ~ \color{green}{\textbf{P}}\text{Q}\color{green}{\textbf{R}} \)

    • one year ago
  27. AccessDenied Group Title
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    So, can you find the length of that side (AC) given this information?

    • one year ago
  28. TommyTrojan Group Title
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    Yes I got 10.5.

    • one year ago
  29. AccessDenied Group Title
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    Correct. :) Now, we just sum the lengths of the sides.

    • one year ago
  30. TommyTrojan Group Title
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    Your VERY helpful, but I have alot more questions if that's all right with you. PS i'll medal you when we're all done, or now if you want.

    • one year ago
  31. AccessDenied Group Title
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    Hmm, how many questions? :)

    • one year ago
  32. TommyTrojan Group Title
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    5 lol

    • one year ago
  33. TommyTrojan Group Title
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    Most of them are just checking though

    • one year ago
  34. AccessDenied Group Title
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    Okay. :)

    • one year ago
  35. TommyTrojan Group Title
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    Ok let's get started then lol. Jeremiah uses bamboo rods to make the frame of a tailless kite. He ties three bamboo rods together to form a right triangle PQR. He then ties another rod from P that meets RQ at a right angle. Segment PS in the figure below represents this rod and it is 4 inches long. Which of the following could be the lengths of segments QS and SR? QS = 2 inches, SR = 8 inches QS = 6 inches, SR = 10 inches QS = 2 inches, SR = 2 inches QS = 4 inches, SR = 12 inches

    • one year ago
  36. TommyTrojan Group Title
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    • one year ago
  37. TommyTrojan Group Title
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    I got A. Is that correct?

    • one year ago
  38. AccessDenied Group Title
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    If I recall this type of situation correctly: PS/ QS = RS/ PS 4 / QS = RS / 4 A) 4/2 = 8/4 ==> 2 = 2. Appears to be correct. :)

    • one year ago
  39. TommyTrojan Group Title
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    OK An architect planned to construct two similar stone pyramid structures in a park. The figure below shows the front view of the pyramids in her plan but there is an error in the dimensions. Which of the following changes should she make to the dimensions to correct her error? change the length of side AB to 2 feet change the length of side PQ to 8 feet change the length of side AB to 1 feet change the length of side PQ to 4 feet

    • one year ago
  40. TommyTrojan Group Title
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    • one year ago
  41. AccessDenied Group Title
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    Hmm, do you have an answer to check?

    • one year ago
  42. TommyTrojan Group Title
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    No this one I don't quite understand.

    • one year ago
  43. AccessDenied Group Title
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    Ah, okay. This is another similar figures question. The key here is having the same side ratios again, similar to some earlier problems. First, I'd check each side ratio to see if there is a sort of "odd-man out."

    • one year ago
  44. AccessDenied Group Title
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    Our corresponding sides: AC ~ PR, AB ~ PQ, BC ~ QR We should check all three of these ratios. AC/PR, AB/PQ, BC/QR

    • one year ago
  45. TommyTrojan Group Title
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    Ok i plugged in the numbers but now what?

    • one year ago
  46. AccessDenied Group Title
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    What do you get for each ratio? Is one of them different?

    • one year ago
  47. TommyTrojan Group Title
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    AB-PQ is the different on it gets 1/2, while all the other ratios get .3 repeated

    • one year ago
  48. AccessDenied Group Title
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    Yep. So, we'd like to find the solution that changes AB or PQ to match the other two side ratios.

    • one year ago
  49. AccessDenied Group Title
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    For this, we could just go through each proposed solution and check to see if it works out.

    • one year ago
  50. TommyTrojan Group Title
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    Is it A?

    • one year ago
  51. AccessDenied Group Title
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    Yes. :)

    • one year ago
  52. TommyTrojan Group Title
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    Ok only 2 more left.

    • one year ago
  53. TommyTrojan Group Title
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    Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 1.8 inches and the length of segment CR is 3.3inches. The distance between A and C is 6.6 inches. What is the distance between the endpoints of the beams P and Q? 3.6 inches 0.9 inches 1.8 inches 2.5 inches

    • one year ago
  54. TommyTrojan Group Title
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    • one year ago
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  55. AccessDenied Group Title
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    Here is another case of similar triangles. Can you identify the side-ratios here? Just to see if you understand the similar triangles have side ratios detail. :)

    • one year ago
  56. TommyTrojan Group Title
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    Oh I forgot to trell you I got A.

    • one year ago
  57. AccessDenied Group Title
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    Ah, okay. A) is correct to me. :) We set up a simple side ratio: QR/PR = AC/PQ' 3.3/1.8 = 6.6/x; x = 6.6 * 1.8 / 3.3 = 3.6

    • one year ago
  58. TommyTrojan Group Title
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    Moris drew two triangles; triangle ABC and triangle PQR, on a coordinate grid. The coordinates of the vertices of triangle PQR are P(-3, -2), Q(-3, -4), and R(-1, -4). The coordinates of the vertices of triangle ABC are A(-3, 4), B(-1, 4), C(-3, 2). Which postulate can be used to prove that the two triangles are congruent? SAS, because AAA, because ASA, because SSS, because

    • one year ago
  59. TommyTrojan Group Title
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    I got D

    • one year ago
  60. AccessDenied Group Title
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    Yeah, I am thinking D) as well. We're given all the points, we could easily just take distance formula or if they're horixontal/vertical, count.

    • one year ago
  61. TommyTrojan Group Title
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    Well I guess that's it, I have more but, since I only said 5 I will keep my word and let you go. OK Thanks though

    • one year ago
  62. TommyTrojan Group Title
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    Thanks BIG TIME!!

    • one year ago
  63. AccessDenied Group Title
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    You're welcome! :)

    • one year ago
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