help w geo?

Question

abcd is a square
a) find the distance from H to each side of the square.
b) find BF, FC, CG, DE, EA, EH and HF.

could somebody help? u dotn needa find all of them for me juts a few w work so i have an understanding of how to find it . ty ;]



[IMG]http://i228.photobucket.com/albums/ee97/krakhead546/lala.jpg[/IMG]

http://i228.photobucket.com/albums/ee97/krakhead546/lala.jpg

http://s228.photobucket.com/albums/ee97/krakhead546/?action=view¤t=lala.jpg


one of these links will show you the picture of the square thansk all

Answer 1

Let us introduce a coordinate system in such a way that the center is in the point D=(0,0), DC is the x axis and DA is the y axis.

Now A=(0, 16), C=(16, 0), B=(16, 16) and G=(12, 0).

a)
Point H is in the center of AG, therefore it’s coordinates are H=(6, 8). Now it’s clear that distance of H from AB and DC is 8 each and distance of H from AD and BC are 6 and 10 respectively.

b)
Triangles AHE and ADG are similar because they have identical angles. Therefore
AH / AE = AD / AG
10 / AE = 16 / 20
AE = 12.5
E=(0, 3.5)

And also
AH / HE = AD / DG
10 / HE = 16 / 12
HE = 7.5

Now let us introduce two more points K=(0, 8) and L=(16, 8).

Triangles HEK and HFL are similar, therefore
HK / KE = HL / LF
6 / 4.5 = 10 / LF
LF = 7.5
F=(16, 15.5)

I think now we have everything important. Yes,
BF = 0.5
FC = 15.5
CG = 4
DE = 3.5
EA = 12.5
EH = 7.5
HF = 12.5

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Answer 2

Interested in this as well

Answer 3

whenever I post a question, even if its the simplest one, they can't offer me a proper informed answer on this site. wtf happened to people that really make the effort to answer??