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dollwonderland January 25th, 2015 05:14 PM

Matrix Problem I am stumped on
 
Find the transformation for the triangle with the given vertices: D(8,15) E(7,-4) F(4,-10) moved right 3 and down 1, then reflected about the x-axis, then rotated 172 degrees counter clockwise. I know the answer, but I don't have any idea how to get it. Answer is D1 = (-8.4, 15.4) E1 = (-10.6, -3.6) F1 = (-8.5, -9.9) Thanks!

USAMO Reaper January 25th, 2015 06:38 PM

first part is easy, add the x and y coordinates of each vertex by 3 and -1 respectively.
now change the sign of the y coordinate of each vertex.
finally, multiply each of the vertex (as a vector) by the rotational matrix
arccos 172 -arcsin 172
arcsin 172 arccos172


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