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Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4)

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mikemcgarry
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Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink] New post   Updated on: 01 Nov 2012, 15:33
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Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4), K = (–2, 1), L = (6, 7), and M = (6, –4). What is its perimeter?

(A) 34
(B) 36
(C) 38
(D) 40
(F) 42

For a discussion of how to handle with elegance both this question and distance in the x-y plane in general see this post. Other experts, feel free to share any other insights about elegance in x-y plane problems.
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Originally posted by mikemcgarry on 01 Nov 2012, 15:30.
Last edited by Bunuel on 01 Nov 2012, 15:33, edited 1 time in total.
Renamed the topic.
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Re: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink] New post   01 Nov 2012, 16:47
i guess it fairly simple and straight fwd use of distance formula and intercept
JK = 5
LM = 11
KL =using distance formula 10
JM = using distance formula 8

Sum of all is 34
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Re: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink] New post   26 Oct 2013, 04:54
mikemcgarry wrote:
Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4), K = (–2, 1), L = (6, 7), and M = (6, –4). What is its perimeter?

(A) 34
(B) 36
(C) 38
(D) 40
(F) 42

For a discussion of how to handle with elegance both this question and distance in the x-y plane in general see this post. Other experts, feel free to share any other insights about elegance in x-y plane problems.



Is there any shortcut to these type of questions than just calculating distance between two points and then adding all of them, that seems bit of time killer for me. But if we dont have any alternative we have to follow the approach.

Regards,
Abhinav
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Re: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink] New post   26 Oct 2013, 11:45
abhinav11 wrote:
mikemcgarry wrote:
Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4), K = (–2, 1), L = (6, 7), and M = (6, –4). What is its perimeter?

(A) 34
(B) 36
(C) 38
(D) 40
(F) 42

For a discussion of how to handle with elegance both this question and distance in the x-y plane in general see this post. Other experts, feel free to share any other insights about elegance in x-y plane problems.



Is there any shortcut to these type of questions than just calculating distance between two points and then adding all of them, that seems bit of time killer for me. But if we dont have any alternative we have to follow the approach.

Regards,
Abhinav


I think all sides are pretty straight forward. The only side that needs calculation is the one that is not parallel to the axis (y and x)
and it can be found using the triangle formula (draw a triangle that originates in the vertices to the base.)
you get 10+8+5+11=34
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Re: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink] New post   26 Oct 2013, 13:16
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abhinav11 wrote:
mikemcgarry wrote:

For a discussion of how to handle with elegance both this question and distance in the x-y plane in general see this post. Other experts, feel free to share any other insights about elegance in x-y plane problems.


Is there any shortcut to these type of questions than just calculating distance between two points and then adding all of them, that seems bit of time killer for me. But if we dont have any alternative we have to follow the approach.

Regards,
Abhinav

Dear Abhinav,
The reason I posted this problem was precisely to demonstrate that an elegant solution was possible. Please follow the link given in the problem to a page that demonstrates this elegant time-saving solution.
Mike :-)
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Re: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink] New post   01 Sep 2021, 09:59
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Re: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4) [#permalink]
01 Sep 2021, 09:59
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