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# Reflect on this

10 replies to this topic

### #1 bonanova

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Posted 15 July 2014 - 07:07 AM

A triangle with vertices (6,5), (8,-3) and (9,1) is reflected about the line x = 8

to create a second, overlapping triangle with vertices at (10,5), (8,-3) and (7,1).

What is their combined area?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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### #2 nana77

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Posted 15 July 2014 - 07:31 AM

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### #3 bonanova

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Posted 15 July 2014 - 08:11 AM

That is the area of a rectangle that contains all the vertices: x in [6, 10] and y in [-3, 5].

The area we need is less than that.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #4 nana77

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Posted 15 July 2014 - 09:03 AM

Did you only want the area of overlap?

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### #5 bonanova

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Posted 15 July 2014 - 09:32 AM

No. It should be included, but only once.

The two triangles (the original and its mirror image) partially overlap,

making a four-sided figure with vertices at (6,5) (8,-3) (10,5) and a point

that is the intersection of lines segments from (6,5) to (9,1) and from (10,5) to (7,1).

We want the area of that four-sided figure.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #6 nana77

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Posted 15 July 2014 - 09:54 AM

Oh. I had a scatter plot to see it and was giving the area of everything in the plot. But there is a piece to subtract out of that.

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### #7 DeGe

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Posted 15 July 2014 - 03:57 PM

Spoiler for Area - overlap

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### #8 witzar

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Posted 15 July 2014 - 04:16 PM   Best Answer

Spoiler for

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### #9 k-man

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Posted 15 July 2014 - 04:19 PM

Spoiler for I get

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### #10 k-man

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Posted 15 July 2014 - 04:21 PM

witzar beat me to it

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