# i have a point X (1,1) that a a transformation M to become X1 (2,1)?

Find the transformation matrix that maps x (1,1) to x1 (2,1), the line y=2x to y=0 and the line y = -x to the line x=0.

Update:

Ok well that fails.

if you tried that matrix on point (1,1) it came out as (0,2) and hance fails.

haha thanks for the opinion thoe.

might wanna try again.

Relevance

First of all, let's write M as a matrix M =

[a b]

[c d]

The the information that x→x1 tells us:

[1]      a + b = 1

[2]      c + d = 2

The fact that y = 2x is sent to y=0 tells us that the point (1,2) is sent to the point (k,0) for some k. We can use that and our M to get

[3]      a + 2b = k

[4]      c + 2d = 0

Finally, the line y = -x gets sent to x=0, so (1,-1) gets sent to (0,p) for some real number p. That tells us (yet again, using our matrix for M) that:

[5]      a - b = 0

[6]      c - d = p

Adding [1] and [5] gives us 2a = 1, or a = 1/2.

Substitute to get b = -1/2.

Subtracting [2] from [4] gives us d=-2.

Substitute top get c = 4.

Notice we never had to bother with finding k or p. We could now, but it is irrelevant. The point is we are done. M =

[ 1/2   -1/2 ]

[ -2       4  ]