1. Transformations

Hi,

When using the dash method for determining transformations, when it says a translation of +2 units parallel to the x axis, does this mean +2 units from the y axis?
So would it be : (x,y) --> (x, y+2)?? Similarly to this, would a dilation of 2 parallel to the x axis, mean dilation 2 from the y axis? (x,y) --> (x, 2y) ?

Could someone please clarify the use of the words parallel or from the x or y axis in regards to the use of this dash method.

Thank you

- ChanelSapphire

2. Re: Transformations

Originally Posted by ChanelSapphire
When using the dash method for determining transformations, when it says a translation of +2 units parallel to the x axis, does this mean +2 units from the y axis?
So would it be : (x,y) --> (x, y+2)?? Similarly to this, would a dilation of 2 parallel to the x axis, mean dilation 2 from the y axis? (x,y) --> (x, 2y) ?
It is a curse of mathematical terminology is that there is no international standard.
The transformation $(x,y)\to(x,y+2)$ simply takes a graph two units up (a positive vertical transformation).
Because the transformed graph "looks" exactly the same with respect to the x-axis but "moved" two units up, we would say that it is parallel to the x-axis.

3. Re: Transformations

Originally Posted by Plato
It is a curse of mathematical terminology is that there is no international standard.
The transformation $(x,y)\to(x,y+2)$ simply takes a graph two units up (a positive vertical transformation).
Because the transformed graph "looks" exactly the same with respect to the x-axis but "moved" two units up, we would say that it is parallel to the x-axis.
Thanks!!
So for this question, would this be correct:
(x,y) --> (x-1,4y+2) ?
so x'= x-1 and y'=4y+2
x= x'+1 y= (y'-2)/4
so the transformed graph would be y = 4(x-1)^3 +2
Is this the correct interpretation of translation parallel to the x and y axis?

4. Re: Transformations

Originally Posted by ChanelSapphire
.
Doing any sort of "bumping" does nothing but aggravate.

Originally Posted by ChanelSapphire
Thanks!!
So for this question, would this be correct:
(x,y) --> (x-1,4y+2) ?
so x'= x-1 and y'=4y+2
x= x'+1 y= (y'-2)/4
so the transformed graph would be y = 4(x-1)^3 +2
Is this the correct interpretation of translation parallel to the x and y axis?
This particular subject has no universally accepted vocabulary. We have no way to know the background material given to you by the instructor/textbook. That is to say that we cannot give you a tutorial.
I have a suggestion for a reference textbook that gives excellence coverage on transformations.
Any good mathematics library should have Modern Geometries by James R. Smart.