Step One
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Find the length of FO (see below)
All of the triangles are equilateral triangles. Label the center as O
FO = FE = sqrt(5) + sqrt(2)
Step Two
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Drop a perpendicular bisector from O to the midpoint of FE. Label the midpoint as J. Find OJ
Sure the Pythagorean Theorem. Remember that OJ is a perpendicular bisector.
FO^2 = FJ^2 + OJ^2
FO = sqrt(5) + sqrt(2)
FJ = 1/2 [(sqrt(5) + sqrt(2)] \
OJ = ??
[Sqrt(5) + sqrt(2)]^2 = [1/2(sqrt(5) + sqrt(2) ] ^2 + OJ^2
5 + 2 + 2*sqrt(10) = [1/4 (5 + 2 + 2*sqrt(10) + OJ^2
7 + 2sqrt(10) = 1/4 (7 + 2sqrt(10)) + OJ^2 Multiply through by 4
28 + 8* sqrt(10) = 7 + 2sqrt(10) + 4 OJ^2 Subtract 7 + 2sqrt From both sides
21 + 6 sqrt(10) = 4OJ^2 Divide both sides by 4
21/4 + 6/4* sqrt(10) = OJ^2
21/4 + 3/2 * sqrt(10) = OJ^2 Take the square root of both sides.
sqrt OJ^2 = sqrt(21/4 + 3/2 sqrt(10) )
OJ = sqrt(21/4 + 3/2 sqrt(10) )
Step three
find h
h = 2 * OJ
h = 2* sqrt(21/4 + 3/2 sqrt(10) ) <<<<<< answer.
Answer:
a) ΔF'G'H' is the image of ΔFGH
b)Center of dilation (7,-1)
c) Scale factor: 
Step-by-step explanation:
Question a
Since the smaller triangle is named F'G'H', it means that, it is the image of triangle FGH.
Question B.
To find the center of dilation, draw straight lines through any two corresponding points.
The straight lines will meet at (7,-1).
This is called the center of dilation.
See graph in attachment.
Question c
The scale factor of the dilation is given by;
1- expand
4p= 24p + 30
2- move 24p to the other side
4p-24p=30
-20p=30
3- Divide
P= -3/2
Hope this helped!
Answer:
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Step-by-step explanation:
