Find the composition of transformations that maps ABCD to EHGF.

[Mathismyweakness]

Can someone please help me and explain what y would be. So I reflected over the x axis and moved 6 to the right which I got the answer x+6 but I am not sure where the shape landed and so I don't know if I move up or down and by how much.

 

[Harry_the_cat]

Ok so take it one step at a time. Where does ABCD end up when you reflect it in the x-axis? Draw it and show us.

 

[pka]

Can someone please help me and explain what y would be. So I reflected over the x axis and moved 6 to the right which I got the answer x+6 but I am not sure where the shape landed and so I don't know if I move up or down and by how much.
View attachment 32855

You want to map $A \to E,\quad B \to F,\quad C \to G,\quad D \to H$​

i.e. $( - 5,2) \to (1,1),\quad ( - 3,4) \to (3, - 1),\quad ( - 2,4) \to (4, - 1),\quad ( - 1,2) \to (5,1)$​

To do that: shift six units to the right; reflect across $x\text{-axis }$; & lift three units up.​

$$$$

 

[Harry_the_cat]

You want to map $A \to E,\quad B \to F,\quad C \to G,\quad D \to H$​

i.e. $( - 5,2) \to (1,1),\quad ( - 3,4) \to (3, - 1),\quad ( - 2,4) \to (4, - 1),\quad ( - 1,2) \to (5,1)$​

To do that: shift six units to the right; reflect across $x\text{-axis }$; & lift three units up.​

$$$$

@pka. I have to question how much your post has helped Mathismyweakness understand how to solve the problem. You have just provided the answer on a platter.

 

[Deleted member 4993]

@pka. I have to question how much your post has helped Mathismyweakness understand how to solve the problem. You have just provided the answer on a platter.

I agree that the answer was given, but I think the @pka's post was cryptic enough that the poster will have to spend considerable effort to decipher it and use it.

 

[Mathismyweakness]

what

 

[Deleted member 4993]

what

What do you mean by what?

In the response #2 you were asked to

Where does ABCD end up when you reflect it in the x-axis? Draw it and show us.

Please do that and look at response #3. Figure out what does that mean. If you do not know - please tell us where you are stuck!

 

[pka]

what

A the risk of having overzealous comments, here is more help.
If you have access to a mathematics library see if you find Modern Geometries by James R Smart.
Chapter two of that text is a good study of geometric transformations.
Given: $f(x,y)=(x+6,y);\;g(x,y)=(x,-y);~\&~h(x,y)=(x,y+3)$.
$\mathcal{T}(x,y)=h\circ g\circ f(x,y)=(?,?)$
$( - 5,2)\xrightarrow{\mathcal{T}}(1,1)$$$

 

[Otis]

I don't know if I move up or down and by how much

lift three units up

Well, pka's direct answer doesn't seem cryptic to me, Subbo!

On the other hand, why would we bother mentioning pka's behavior in the forum anymore. I doubt that it'll ever change for the better.



$\;$

 

[Harry_the_cat]

A the risk of having overzealous comments, here is more help.
If you have access to a mathematics library see if you find Modern Geometries by James R Smart.
Chapter two of that text is a good study of geometric transformations.
Given: $f(x,y)=(x+6,y);\;g(x,y)=(x,-y);~\&~h(x,y)=(x,y+3)$.
$\mathcal{T}(x,y)=h\circ g\circ f(x,y)=(?,?)$
$( - 5,2)\xrightarrow{\mathcal{T}}(1,1)$$$

Overzealous comment coming up ...

I know this is a very mathematical and symbolic way of approaching the problem and most of us helpers here can handle that level of abstraction.

But... Mathismyweakness' name tells us a lot about where he/she is coming from.

Isn't it easier, at that level, to draw it out on paper and keep it relatively concrete?

 

[Harry_the_cat]

@Mathismyweakness, how have you gone with this problem?? Let us know.

 

[Deleted member 4993]

Overzealous comment coming up ...

I know this is a very mathematical and symbolic way of approaching the problem and most of us helpers here can handle that level of abstraction.

But... Mathismyweakness' name tells us a lot about where he/she is coming from.

Isn't it easier, at that level, to draw it out on paper and keep it relatively concrete?

I think I see pka's motivation.

You provided the next logical concrete action item for the student - but there was no response from the student. So, to prod the student he showed - I assume - the final goal. It is somewhat like looking at the answer of a difficult problem and "the way to approach" it jumps out.