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.
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.
- сhееsеr1Lv 71 decade agoFavorite Answer
First of all, let's write M as a matrix M =
The the information that x→x1 tells us:
 a + b = 1
 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
 a + 2b = k
 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:
 a - b = 0
 c - d = p
Adding  and  gives us 2a = 1, or a = 1/2.
Substitute to get b = -1/2.
Subtracting  from  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 ]