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# Geometry

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Let Q be the center of equilateral triangle ABC. A dilation centered at Q with scale factor -4/3 is applied to triangle ABC, to obtain triangle A'B'C'. Let S be the area of the region that is contained in both triangles ABC and A'B'C'. Find A/[ABC].

Any help would be greatly appreciated! Thanks!

Feb 20, 2021

#1
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I do not understand what a dilation of -4/3 is... does the triangle get smaller?

Feb 20, 2021
#5
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No, the triangle gets larger but it's turned upside-down because of a negative scale factor.

Guest Feb 20, 2021
#2
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I'm pretty sure that the answer can be simplified to [A'B'C']/[ABC]. But from here I'm stuck...

Feb 20, 2021
#4
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I also think that A is a hexagon, but I don't know what to do with this information.

Guest Feb 20, 2021
#3
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Here's a similar question:

https://web2.0calc.com/questions/help_54234#r3

That's gonna look like this:

Feb 20, 2021
edited by Dragan  Feb 20, 2021
#6
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Thanks . However I do not understand if if there is a specific equation that should be used?

Guest Feb 21, 2021
#7
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Let Q be the center of the equilateral triangle ABC. A dilation centered at Q with scale factor -4/3 is applied to triangle ABC, to obtain triangle A'B'C'. Let S be the area of the region that is contained in both triangles ABC and A'B'C'. Find S/[ABC].

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If the side length of a triangle ABC is 3 units then the length of a side of triangle A'B'C' is 4 units.

Step 1/    Find the area of the 3 smallest triangles. Let Z be the total area of these 3 triangles.

Step 2/    Find the area of a triangle ABC.

Step 3/    Find S          S = [ABC] - Z

Answer:            S / [ABC] = ?

Guest Feb 22, 2021
#8
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I'm confused... what does Z equal? (sorry if this is too many questions...)

Guest Feb 24, 2021