Math Is Fun Forum

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

geometry problems

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?

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: geometry problems

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

but i don't really understand the first problem

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: geometry problems

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

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

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Genius is one percent inspiration and ninety-nine percent perspiration

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

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

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: geometry problems

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

so how many different ways are there

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Genius is one percent inspiration and ninety-nine percent perspiration

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

is it still five

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: geometry problems

five more!

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

so is the answer 10?

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: geometry problems

That's what I think.

B

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: geometry problems

thanks, its correct

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Genius is one percent inspiration and ninety-nine percent perspiration