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.

1 Answer

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  • 1 decade ago
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    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  ]

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