1. ## Re: Transformations

Originally Posted by Melody2
I presented you with a well written problem. None of you could answer it.
The reason you didn't get a full answer is not that we can't do the problem, it's because we want you to make the logical connections yourself. This is a well established teaching method. Perhaps it doesn't quite work for you but if we start just handing out answers then we are not doing our jobs IMHO. This is standard policy here and is only broken in few cases.

chiro: Can you show us what you have tried? Have you tried making the answer visual [i.e. drawing it]?

chiro: What about the attempts for the rotations and dilations?

chiro: "When you rotate around a point you subtract the point and then rotate the point counterclockwise by some angle. Have you looked at sines and cosines before?

Plato: There is a well-known transformation across the y-axis: $\displaystyle (x,y) \to (x',y') = \left\{ \begin{array}{l}x' = - x\\y' = y\end{array} \right.$

topsquark: Chiro is giving you a list of transformations you want to look for.

chiro: I'm not being cryptic - take a look at the rotation matrix in two dimensions for more information.

Plato: There is no reason for rotations, reflection about y=x, or dilations.

How is this discussion not helpful? We are trying to give you a chance at solving the problem as well as what to consider if you see similar problems in the future. You have had any number of opportunities to say "I don't follow what you are saying." I am not trying to insult you, simply to show you the nature of the discussion.

-Dan

2. ## Re: Transformations

Originally Posted by romsek
I'm curious how you were able to figure this out. After toying with it for a while I suspected you'd need to move the shape off of (5,0) and rotate it but I wouldn't have come up with that dilation trick in a million years.
Hi Romsek,

Yes I am more than happy to explain my thought processes.

First I did the reflection. This was intuitive but it seemed right because it was then in an orientation so that when it was rotated anticlockwise it would have D on the top.

Now I just looked at the B point because it started and finished on the y axis and the x axis respectively, I guessed that there would be an anticlockwise rotation of 90 degrees involved. But there obviously had to be a dilation to get B into the correct position first.
Now when B was rotated about (5,0) it would need to be on the x axis.
So I draw the line x=5. B would need to be moved to a point on that line.

I then turned my attention to the dilation that would be needed.
I drew a line from the centre of the dilation (-5,0) through B’ and subtended it till it intersected with x=5
That point of intersection would need to be the new B value. i.e. B’’

B’ was the point (0,9.5)
I could see from the diagram that B” was the point (5,19)
So it was clear that B’’ had to be twice as far as B’ from the centre of the dilation.
So I needed a dilation factor of 2
Now I did the dilation and the 3rd star was born.

Now I just had to rotate it 90 degrees anticlockwise to get B onto the y axis.

Lastly I had to counter the enlargement so I implemented a dilation of 0.5 centred at (-5,0)

ALL DONE

Here is the diagram:

3. ## Re: Transformations

Thank you for your response Dan,
Here is my response:

Originally Posted by topsquark
The reason you didn't get a full answer is not that we can't do the problem,
There was never any indication from any of you that you knew how to do the problem.
Quite the opposite, Plato stated that the question made “NO SENSE” and Dan, you said “I agree with Plato”

Originally Posted by topsquark
it's because we want you to make the logical connections yourself. This is a well established teaching method. Perhaps it doesn't quite work for you but if we start just handing out answers then we are not doing our jobs IMHO.
Well it is difficult to hand out answers when you state, or agree with the statement, that the question makes “NO SENSE”

Originally Posted by topsquark
This is standard policy here and is only broken in few cases.
The standard policy is to teach. This is a good policy. Perhaps if you had known how to do the question you may have tried to guide me to an answer.
But since you agreed that “The question makes NO SENSE” It would have been impossible for you to guide me to an answer.

Originally Posted by topsquark
chiro: Can you show us what you have tried? Have you tried making the answer visual [i.e. drawing it]?
I did this

Originally Posted by topsquark
chiro: What about the attempts for the rotations and dilations?

Originally Posted by topsquark
chiro: "When you rotate around a point you subtract the point and then rotate the point counterclockwise by some angle. Have you looked at sines and cosines before?

Originally Posted by topsquark
Plato: There is a well-known transformation across the y-axis: $\displaystyle (x,y) \to (x',y') = \left\{ \begin{array}{l}x' = - x\\y' = y\end{array} \right.$
You have omitted the Plato's most important quote:
“I HAVE NOT TRIED HELPING BECAUSE THE QUESTION MAKES NO SENSE TO ME”

Originally Posted by topsquark
topsquark: Chiro is giving you a list of transformations you want to look for.
The transformations that I had to use were written in the question.

Originally Posted by topsquark
chiro: I'm not being cryptic - take a look at the rotation matrix in two dimensions for more information.
This is in the pre-university section of the forum. There is no reason for chiro to think I had any knowledge of these.
This was a high school transformation question and a knowledge of matrix rotations was most certainly not needed for the answer.

Originally Posted by topsquark
Plato: There is no reason for rotations, reflection about y=x, or dilations.
Of course there was a reason - the question requested it.
“I have not tried helping because the question makes no sense to me”
Plated stated very plainly that he had no idea how to answer the question!

Originally Posted by topsquark
How is this discussion not helpful? We are trying to give you a chance at solving the problem as well as what to consider if you see similar problems in the future. You have had any number of opportunities to say "I don't follow what you are saying." I am not trying to insult you, simply to show you the nature of the discussion.
I did. I said “You are being very cryptic Chiro and … it is not helping”

-------------------------------

In the past I have always enjoyed my time at this site. And I have likely had help from each of you that I have greatly appreciated. I have enormous respect for each and every long term answerer at this site.
But please remember that some/most question askers are seriously trying to learn and understand and many have a great love of mathematics that you should be trying to nurture.
I agree that answers should not be given too readily, especially not to new members who have not yet demonstrated their passion for mathematics. But as mathematicians you should be nurturing mathematical passion. Not setting yourselves above the question askers and treating them with condescension and derision. You cannot teach via humiliation.
ALSO
If you do not know how to do a problem it is not a terrible thing to just politely admit it. You could then work with the asker and perhaps the two of you can learn and work out the answer together. I think, that without admitting it, this is what chiro was trying to do.
It would have been so much nicer if Chiro was just up font about it in the first place! I would have liked to think tank with him.

-Dan[/QUOTE]

4. ## Re: Transformations

There is an error in my explanation #17 It is on the second line of the explanation.
Old wording "Now I just looked at the B point because it started and finished on the y axis and the x axis respectively,"

Better wording "Now I just looked at the B point because in order for the final reduction transformation to work, B had to first be positioned on the x axis.
I had to get B to the negative x axis....." mmm the wording is still not great but the reader can probably join the dots.

5. ## Re: Transformations

Another small error in my explanation. #17
Second last line.
It says: "Now I just had to rotate it 90 degrees anticlockwise to get B onto the y axis."
Of course it should say:
Now I just had to rotate it 90 degrees anticlockwise to get B onto the x axis.

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