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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

1. Point Q is the image of point P under a dilation with center O and scale factor 4. If PQ = 18, then what is OP?

2.We cut a regular pentagon out of a piece of cardboard, and then place the pentagon back in the cardboard.

How many different ways can we place the pentagon back in the cardboard, if we are allowed to rotate but not reflect the pentagon?

3.How many different ways can we place the pentagon back in the cardboard, if we are allowed to rotate and reflect the pentagon?

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,097

hi mathstudent2000

OPQ is a straight line so call OP = x .... We know that PQ = 18 so OQ = x + 18

So make an equation using the scale factor and solve for x.

Label one side AB. If you cannot turn the pentagon over then once you have placed side AB, all the other sides are fixed in place too. So how many ways can you place AB?

If you can turn it over then placing BA is a new way. So how many extra ways does that give you?

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

but i don't really understand the first problem

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
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A dilation is what I call an enlargement. O is fixed and P is stretched out away from O by an amount so that its distance increases by times 4

So OP x 4 = OQ.

Using the x and 18 you can form an equation for x and solve it. (hopefully )

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

for no. 2 i got 5 and for no. 1 i got 6 but i don't know about no.3

Genius is one percent inspiration and ninety-nine percent perspiration

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

i don't get about how many ways you can get when you can also reflect

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,097

Those answers, 5 and 6, are correct.

If you place the hole in the cardboard so there's a vertex at the top, and always read the letters clockwise then the first 5 answers are

ABCDE

BCDEA

CDEAB

DEABC

EABCD

Now flip the pentagon over.

AEDCB

etc

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

so how many different ways are there

Genius is one percent inspiration and ninety-nine percent perspiration

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

is it still five

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,097

five more!

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

so is the answer 10?

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,097

That's what I think.

B

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

thanks, its correct

Genius is one percent inspiration and ninety-nine percent perspiration

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