The triangle A with coordinates (3,2) (5,4) (7,4) can be mapped on to triangle D with a transformation matrix P. Find coordinates of D?

the transformation matrix for P is (""^0 ""_(1) ""^(-1) ""_(0))

1 Answer
Jan 19, 2018

(-2,3), (-4,5) and (-4,7)

Explanation:

Triangle A is mapped to D via a Transformation matrix bbP, so given the column vector coordinates of A, bb ul a, bb ul b and bb ul c, say, we can write the destination coordinate as:

bb ul (a)' = bb Pbb ul a , \ \ bb ul (b)' = bb P bb ul b , and , \ \ bb ul (c)' = bb Pbb ul c ,

Given the coordinates (3,2), (5,4) and (7,4) and the matrix bb P= ( (0,-1), (1,0)) we can write in matrix form as

bb D = ( (0,-1), (1,0)) ( (3,5,7), (2,4,4) )

\ \ \ = ( (0*3-1*2, 0*5-1*4, 0*7-1*4), (1*3+0*2, 1*5+0*4, 1*7+0*4) )

\ \ \ = ( (-2, -4, -4), (3, 5, 7) )

And so the respective coordinates of D are:

(-2,3), (-4,5) and (-4,7)

And we can view the transformation graphically:
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We can conclude that the matrix transformation represents an anti-clockwise rotation of 90^o about the origin.