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weirdguy66

Guest

transformations

i dont know how this question wants me to write the answer

the co-ordinates of shape p are (2,1)(2.5,2)(2,3)(1.5,2). the new co-ordinates of shape p are (4,2)(5,4)(4,6)(3,4). describe fully the single transformation that maps shape p onto shape q.

i dont get this question. should i use a matrix (matrices) to describe it? plus i dont know how to describe enlargement. i think it moves 4 right and 2 up, i know how to do that in matrices. but i dont know how to describe the enlargement. i think that is enlargement is that the area squares itself to make q, but i really need help.

thanks

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: transformations

in terms of describing, you could just say 'enlargment of factor .... relative to the point (...,...)' or something,

looking simply at the coordinates, it is simply an enlargement of factor 2 about the origin:

you can ignore all of the below, it is simply if you want to learn a bit more about transformations)

as a matrix, using homogoneuos coordinates, a translation matrix looks like this for a coordinate in 2D

where tx,ty are your translations

a scaling matrix, to scale relative to (0,0) would look like:

where sx,sy are your horizontal and vertical scale factors

an 'enlargement' matrix about some other point would be a combination of 3 matrices:

where px,py is the coordinate for the enlargement, and sx,sy are the scale factors, multiplying that out gives a matrix like this:

which when multiplied by a coordinate gives:

Last edited by luca-deltodesco (2007-06-05 07:48:59)

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