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#1 2012-12-09 09:13:24

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Transformations

Hi,

I am really stuck on how to rotate the following

Rotate the triangle 270 clockwise around (0,0).

View Image: refl7.jpg

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#2 2012-12-09 09:44:56

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

Re: Transformations

hi zee-f

When you rotate 270 clockwise, that's the same as 90 anticlockwise.  (90, 180, 270, 360)

Look at the point (2,1)  I've boxed it into a rectangle and then showed the whole rectangle rotating.

That corner moves to (-1,2)  For 90 degrees that sort of thing always happens.  The x and y coordinates swap over and one becomes negative.

It happens because the across distance in the rectangle becomes the up distance and the up becomes the across (but now going to the left ... ie. it is now a negative amount).

2 ----> -1
1 ---->  2

So you should be able to do the other points the same way. 

Bob

View Image: zeef rotation.gif

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

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#3 2012-12-10 03:26:16

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Transformations

I rotated the paper  270 clock wise so 3 times clockwise and I got

View Image: refl17.jpg

One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#4 2012-12-10 06:27:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,695

Re: Transformations

Hi zee-f;

That is correct!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2012-12-10 06:27:37

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

Re: Transformations

hi zee-f,

That looks good to me,  smile

Bob


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

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#6 2012-12-10 08:18:03

zee-f
Member
Registered: 2011-05-12
Posts: 1,220

Re: Transformations

I choose B and it was incorrect but why doesn't the angle change because  the size is getting bigger.

1. An angle changes in size as it undergoes a dilation.
A False
BTrue


One, who adopts patience, will never be deprived of success though it may take a long time to reach him. Imam ali (as)<3

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#7 2012-12-10 08:28:22

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,695

Re: Transformations

Hi;

The sides are dilated by a common factor but the ratios of the sides remain the same. In plain english the triangle will look the same just bigger.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#8 2012-12-10 10:21:47

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,394

Re: Transformations

hi zee-f

I call it an enlargement but it is the same as a dilation.

I made a triangle ABC.

Then I made it bigger  = DBE

The angles stay the same.

Bob

View Image: zeef dilation.gif

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

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