Transformation (rotation&enlargement)

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December 27th 2008, 06:47 PM
nikk

2 Attachment(s)

Transformation (rotation&enlargement)

i already done this problem but i have some problem on the following question because my ans is not same as per book, so i need to confirm the ans by the expert here :

Attachment:
As below
left-question diagram
right - my solution

Question:
Quadrilateral GHIJ is the image of quadrilateral PQRS under a transformation V followed by a transformation W. Specify the transformation V and W.

ANS(from book)

V is a rotation of 90 degree anticlockwise about ( 6,5)
W is an enlargement with centre at ( 4,7) and a scale factor of 2.

tq for your time to help me
December 27th 2008, 06:54 PM
kalagota

what is your answer? basically, the two drawings are similar..
December 27th 2008, 07:05 PM
nikk

Quote:

Originally Posted by kalagota

what is your answer? basically, the two drawings are similar..

tq for your quick reply....

according to my attachment drawing (right hand site-green greed line), it shown the intersection which is a coordinate of rotation.
you can refer it clearly here:
http://www.mathhelpforum.com/math-he...ent-my-ans.jpg

my ans look like have the decimal value( 4.+++, 5.+++) and already out from the given ans.

do u have any solution or software on transformation topic???
December 27th 2008, 07:15 PM
kalagota

Quote:

Originally Posted by nikk

my ans look like have the decimal value( 4.+++, 5.+++) and already out from the given ans.

i min, yes.. but that vague. you were asked to find V and W.. your answer doesn't make sense yet as it is.. where does your coordinate refer to?

Quote:

Originally Posted by nikk

do u have any solution or software on transformation topic???

nope.. but i think we can solve it analytically.. :)
December 27th 2008, 07:36 PM
nikk

Quote:

Originally Posted by kalagota

i min, yes.. but that vague. you were asked to find V and W.. your answer doesn't make sense yet as it is.. where does your coordinate refer to?

nope.. but i think we can solve it analytically.. :)

i still can't make the answers on V because when i compare my answer ans wrong :
the book answers on point of intersection which is ( 6,5) from the book and my answer is on point of intersection ( 4.+++, 5.+++) [ i just round it from the graf which is i upload]

so it mean i can't get the
- angle of rotation and
- direction of rotation (anticlockwise or clockwise)

because i still can't get the point of intersection which is ( 6,5).

hope it will help you sir
December 27th 2008, 07:50 PM
kalagota

well, maybe your software only gives you one transformation. but you were told that the transformation is composed of two transformation..

here are some observation from the original graph:
first, notice $PS$ and $GJ$ .. basically, from horizontal, it became vertical.. you may infer that there is an multiple of $90^\circ$ rotation. but of course, you should have been taught that $90^\circ$ rotation clockwise is the same as $270^\circ$ rotation anticlockwise or $90^\circ$ rotation anticlockwise is the same as $270^\circ$ rotation clockwise; you may infer indirectly that it must be a $90^\circ$ rotation anticlockwise.. problem1: where is the center of rotation?

second, see that $|GJ|=2|PS|$ .. so there must be an enlargement with 2 as a factor.. problem2: where is the center of enlargement?

if you were able to answer problem1, then problem2 can easily be answered by some observations..

hope, this would help you..
December 27th 2008, 08:00 PM
nikk

Quote:

Originally Posted by kalagota

well, maybe your software only gives you one transformation. but you were told that the transformation is composed of two transformation..

here are some observation from the original graph:
first, notice $PS$ and $GJ$ .. basically, from horizontal, it became vertical.. you may infer that there is an multiple of $90^\circ$ rotation. but of course, you should have been taught that $90^\circ$ rotation clockwise is the same as $270^\circ$ rotation anticlockwise or $90^\circ$ rotation anticlockwise is the same as $270^\circ$ rotation clockwise; you may infer indirectly that it must be a $90^\circ$ rotation anticlockwise.. problem1: where is the center of rotation?

second, see that $|GJ|=2|PS|$ .. so there must be an enlargement with 2 as a factor.. problem2: where is the center of enlargement?

if you were able to answer problem1, then problem2 can easily be answered by some observations..

hope, this would help you..

yap.. i agree about $PS$ and $GJ$ .. basically, from horizontal, it became vertical.. you may infer that there is an multiple of $90^\circ$ rotation. but of course, you should have been taught that $90^\circ$ rotation clockwise is the same as $270^\circ$ rotation anticlockwise or $90^\circ$ rotation anticlockwise is the same as $270^\circ$ rotation clockwise; you may infer indirectly that it must be a $90^\circ$ rotation anticlockwise..

but i also gave problem to verify that ( 6,5) as the center of rotation..because i can't get it according to my attachment answers...

can u get ( 6,5) as the center of rotation

thank
December 27th 2008, 09:27 PM
kalagota

i didn't actually solve it (since it is tedious) but here are some hints: you can get the similarity transformation $T(\alpha)$ with similarity ratio equal to 2; and and use the fact that $V=C(90^\circ)$ where $C$ is the center of rotation and $W=2D$ is an enlargement translation about a center $D$ . thus $T(\alpha) = W\circ V=2D \circ C(90^\circ)$ .

well, it is indeed tedious. besides, we were not asked to solve problems like this before but at least, we should know the process. hope this help..

or maybe, other people out there knows how to do this with simpler approach.. :)