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TommyTrojan
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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
 one year ago
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
 one year ago

This Question is Closed

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
@KonradZuse @AccessDenied
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Have you tried plotting the points that you were given?
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Yes, but I still don't get it
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Could you post that graph here? :)
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
I actually wrote it on loose leaf paper lol. Soz
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
But how would you do it?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
OK can I ask you a few more?
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Its either a or b
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
OK thank you lol no problem
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
PQ = AB QR = BC PR = AC
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
So it is either a or b
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
I got a. Is that right?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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 twovariable system. This one is pretty simple to "see" though.
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
I have a few more questions, if that's all right with you?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
I think we'd get two solutions, one would be some sort of fraction or rational and (1,4) also.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Sure, that's fine. :)
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
I got B, just checking my work.
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
@AccessDenied
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
How did you get B)?
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Tell you the truth, I guessed, i'm confused on how to do it.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
So, can you find the length of that side (AC) given this information?
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Yes I got 10.5.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Correct. :) Now, we just sum the lengths of the sides.
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Hmm, how many questions? :)
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Most of them are just checking though
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Okay. :)
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
I got A. Is that correct?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Hmm, do you have an answer to check?
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
No this one I don't quite understand.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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 "oddman out."
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Ok i plugged in the numbers but now what?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
What do you get for each ratio? Is one of them different?
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
ABPQ is the different on it gets 1/2, while all the other ratios get .3 repeated
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Yep. So, we'd like to find the solution that changes AB or PQ to match the other two side ratios.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
For this, we could just go through each proposed solution and check to see if it works out.
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Is it A?
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Yes. :)
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Ok only 2 more left.
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
Here is another case of similar triangles. Can you identify the sideratios here? Just to see if you understand the similar triangles have side ratios detail. :)
 one year ago

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Oh I forgot to trell you I got A.
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
I got D
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
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

TommyTrojan Group TitleBest ResponseYou've already chosen the best response.0
Thanks BIG TIME!!
 one year ago

AccessDenied Group TitleBest ResponseYou've already chosen the best response.1
You're welcome! :)
 one year ago
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