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# transformation of a plane to a line using a matrix watch

1. Hi,

I'm told that the matrix T is:

I'm also told that:

has equation

I'm asked to show that the image of under is a line and to find Cartesian equations of this line.

I understand that I should:

Let and , therefore

Therefore the general point on can be written as:

So I can now find :

I want to find the Cartesian equation of this, so I say:

Let

By using simultaneous equations I know that:

So the Cartesian equations of the image of are:

Now this is where I start to get a bit confused. My book now says:

"Let
Then, as , we can say ,
The Cartesian equations can be written as:

"

Now, I understand the basic manipulation to get to this point, but they're dividing by 0. Why and how are they doing this?

Thank you

P.S. Sorry that this question is so long.
2. Doesn't it just mean that the line lies in the plane given by x=-6? Then you have "0/0" = y/1 = z+12/1
3. ... if b_1 is zero it's saying x doesn't change as you vary so it is always x=-6 and so the line lies in the plane given by x=-6.
4. (Original post by steve44)
... if b_1 is zero it's saying x doesn't change as you vary so it is always x=-6 and so the line lies in the plane given by x=-6.
Right, that makes sense thank you! I think I just saw "divide by zero" and panicked

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Updated: January 21, 2014
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