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TommyTrojan

  • 2 years ago

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)

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  1. TommyTrojan
    • 2 years ago
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    @KonradZuse @AccessDenied

  2. AccessDenied
    • 2 years ago
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    Have you tried plotting the points that you were given?

  3. TommyTrojan
    • 2 years ago
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    Yes, but I still don't get it

  4. AccessDenied
    • 2 years ago
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    Could you post that graph here? :)

  5. TommyTrojan
    • 2 years ago
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    I actually wrote it on loose leaf paper lol. Soz

  6. TommyTrojan
    • 2 years ago
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    But how would you do it?

  7. AccessDenied
    • 2 years ago
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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...

  8. TommyTrojan
    • 2 years ago
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    OK can I ask you a few more?

  9. TommyTrojan
    • 2 years ago
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    Its either a or b

  10. AccessDenied
    • 2 years ago
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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.

  11. TommyTrojan
    • 2 years ago
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    OK thank you lol no problem

  12. AccessDenied
    • 2 years ago
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    PQ = AB QR = BC PR = AC

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  13. TommyTrojan
    • 2 years ago
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    So it is either a or b

  14. AccessDenied
    • 2 years ago
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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

  15. TommyTrojan
    • 2 years ago
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    I got a. Is that right?

  16. AccessDenied
    • 2 years ago
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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.

  17. TommyTrojan
    • 2 years ago
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    I have a few more questions, if that's all right with you?

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

  19. AccessDenied
    • 2 years ago
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    Sure, that's fine. :)

  20. TommyTrojan
    • 2 years ago
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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

  21. TommyTrojan
    • 2 years ago
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  22. TommyTrojan
    • 2 years ago
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    I got B, just checking my work.

  23. TommyTrojan
    • 2 years ago
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    @AccessDenied

  24. AccessDenied
    • 2 years ago
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    How did you get B)?

  25. TommyTrojan
    • 2 years ago
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    Tell you the truth, I guessed, i'm confused on how to do it.

  26. AccessDenied
    • 2 years ago
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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. \( \color{green}{\textbf{A}}\text{B}\color{green}{\textbf{C}} ~ \color{green}{\textbf{P}}\text{Q}\color{green}{\textbf{R}} \)

  27. AccessDenied
    • 2 years ago
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    So, can you find the length of that side (AC) given this information?

  28. TommyTrojan
    • 2 years ago
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    Yes I got 10.5.

  29. AccessDenied
    • 2 years ago
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    Correct. :) Now, we just sum the lengths of the sides.

  30. TommyTrojan
    • 2 years ago
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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.

  31. AccessDenied
    • 2 years ago
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    Hmm, how many questions? :)

  32. TommyTrojan
    • 2 years ago
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    5 lol

  33. TommyTrojan
    • 2 years ago
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    Most of them are just checking though

  34. AccessDenied
    • 2 years ago
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    Okay. :)

  35. TommyTrojan
    • 2 years ago
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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

  36. TommyTrojan
    • 2 years ago
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  37. TommyTrojan
    • 2 years ago
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    I got A. Is that correct?

  38. AccessDenied
    • 2 years ago
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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. :)

  39. TommyTrojan
    • 2 years ago
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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

  40. TommyTrojan
    • 2 years ago
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  41. AccessDenied
    • 2 years ago
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    Hmm, do you have an answer to check?

  42. TommyTrojan
    • 2 years ago
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    No this one I don't quite understand.

  43. AccessDenied
    • 2 years ago
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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."

  44. AccessDenied
    • 2 years ago
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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

  45. TommyTrojan
    • 2 years ago
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    Ok i plugged in the numbers but now what?

  46. AccessDenied
    • 2 years ago
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    What do you get for each ratio? Is one of them different?

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

  48. AccessDenied
    • 2 years ago
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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.

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

  50. TommyTrojan
    • 2 years ago
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    Is it A?

  51. AccessDenied
    • 2 years ago
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    Yes. :)

  52. TommyTrojan
    • 2 years ago
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    Ok only 2 more left.

  53. TommyTrojan
    • 2 years ago
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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

  54. TommyTrojan
    • 2 years ago
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  55. AccessDenied
    • 2 years ago
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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. :)

  56. TommyTrojan
    • 2 years ago
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    Oh I forgot to trell you I got A.

  57. AccessDenied
    • 2 years ago
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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

  58. TommyTrojan
    • 2 years ago
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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

  59. TommyTrojan
    • 2 years ago
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    I got D

  60. AccessDenied
    • 2 years ago
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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.

  61. TommyTrojan
    • 2 years ago
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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

  62. TommyTrojan
    • 2 years ago
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    Thanks BIG TIME!!

  63. AccessDenied
    • 2 years ago
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    You're welcome! :)

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