ok im having more trouble with this one problem then i should.
the question states:
Perform the stated transformation on the preimage, ABC. Give the coordinates of the image, A'B'C'.
the coords for ABC are
A:(-1,-3)
B:(1,1)
C:(5,-1)
im supposed to do a rotation of 270 degrees clockwise about the origin

- anonymous

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- inkyvoyd

so (x,y) to (-x,-y)

- anonymous

ok so A=(1,3), B=(-1,-1) and c = (-5,1)

- inkyvoyd

yeah

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- anonymous

alright cool thanks

- terenzreignz

Wait...

- terenzreignz

While the concept is 'pretty much' straightforward, I would like to point out that negating both coordinates is a rotation of *180 degrees* about the origin and not 270.

- anonymous

ok so add another 90 degrees and what do i get

- anonymous

b=(-1,1)
a=(1,-3)
c=(5,1)

- terenzreignz

I'm sure you have a definite formula for a rotation by 90 degrees...
Think about it.... to rotate by 270 degrees, you can think about it as FIRST rotating by 180 degrees (which you already know how to) and THEN rotating by 90 degrees.

- anonymous

right so it would be similar to this? |dw:1378421051079:dw|

- inkyvoyd

sorry @splatter6 @terenzreignz is in fact right; feel free to give him a medal instead hehe

- anonymous

its alright dude you still helped me get there 3/4's of the way

- terenzreignz

Roughly... yes...|dw:1378421112380:dw|

- terenzreignz

Understandably, this is confusing.
I'd like to first point out that the first transformation, the one by 90 degrees only:|dw:1378421333956:dw|

- terenzreignz

Involves switching the coordinates, and THEN negating the new x-coordinate (which in this case, happened to be y. Don't get confused)

- anonymous

label the points for me please

- terenzreignz

They ARE labeled... -.-

- anonymous

no i mean A,B,C

- terenzreignz

There's no need for that, just pay attention:
Look, to rotate a point about the origin 90 degrees, say you originally have
(p,q)
What you do is switch the two coordinates:
(q,p)
and then NEGATE the first coordinate:
(-q,p)
and THAT is one rotation of 90 degrees.
To rotate by 270, just perform this transformation three times on each point.

- anonymous

so once you negate the coords it then becomes the 180 or just 90 degrees

- terenzreignz

If you negate both coordinates, (without switching them, that is) that's 180 degrees.
So you could do THAT first, and then rotate by 90 degrees using that process described above. ^

- anonymous

so i will take A for example
A=(-1,-3)=(-3,-1)=(3,-1)and that will be the full 270 degrees?

- terenzreignz

Okay... time out:
To rotate (p,q) by 270 degrees, you may do either of the following:
FIRST WAY
Step 1
Rotate by 180 degrees by ONLY negating both coordinates (no switching!)
Step 2
Rotate by 90 degrees using the process described above.
SECOND WAY
Just rotate by 90 degrees THREE times using the process described above.

- terenzreignz

Either way you use, you should end up with the same answer.

- anonymous

ok so then A=(-1,-3)=(1,3)this is 180 now to get the full 270 A=(1,3)=(3,1)

- terenzreignz

Almost ^_^
Unfortunately, *almost* is rather indistinguishable from 'wrong'
Your first transformation is correct, the rotation by 180 degrees.
However, you forgot that when rotating by 90 degrees, not only do you switch the coordinates, but you should also have *negated the new first (left) coordinate*
Try again...
You're almost there...

- anonymous

ok so then A=(-3,1)

- terenzreignz

Excellent :)
Sorry for putting you through all that... your reward:
A shortcut ^_^
To transform by 270 degrees, simply switch the two coordinates and then negate *the new SECOND coordinate*
As you can see...
(-1,-3)
Switch --> (-3,-1)
Negate the *second coordinate* --> (-3,1)
Cheers :D

- anonymous

dude you didn't put me through anything but me learning how to do math so i don't fails if anything i should be sorry for taking up your time so many a thanks

- terenzreignz

Though... you could post your answers to the other two points... if you're willing ^_^

- anonymous

B=(-1,1)
C=(1,5)
right?

- terenzreignz

Nope... those are just 90 degree rotations...
I already gave you the shortcut... if it confuses you, just do what you did with the first point again.

- anonymous

is B=(-1,1) correct?

- anonymous

C=(-1,5)

- terenzreignz

Are you guessing? That won't do... check the shortcut I gave you again.

- anonymous

no i'm not guessing
B=(1,1)=(1,1)[that was a switch but since they're both 1's it doesn't matter lol]=(-1,1)

- terenzreignz

But I told you... switching then negating the first coordinate is a 90 degree rotation, not a 270 one.

- anonymous

C=(5,-1)=(-1,5)=(-1,5)

- anonymous

but you said To transform by 270 degrees, simply switch the two coordinates and then negate *the new SECOND coordinate*

- terenzreignz

yes... and which one is the second coordinate?

- terenzreignz

You negated the new FIRST coordinate.

- terenzreignz

If you haven't noticed yet, it's the left one's you've been negating...

- anonymous

so then B=(1,-1)
and C=(-1,-5)

- terenzreignz

Much better.
Pay attention to details.
Signing off.
----------------------
Terence out

- anonymous

thanks dude

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