SOLUTION: Name the single translation that can replace the composition of these three translations: (x,y)→(x+2,y+3), then (x,y)→(x-5,y+7), then (x,y)→(x+13,y).

Question 1062502: Name the single translation that can replace the composition of these three translations: (x,y)→(x+2,y+3), then (x,y)→(x-5,y+7), then (x,y)→(x+13,y).
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

(x,y)→(x+2,y+3),

That adds +2 to the first coordinate, and adds +3
to the second coordinate

 then (x,y)→(x-5,y+7),

That adds -5 to the first coordinate, and adds +7
to the second coordinate

 then (x,y)→(x+13,y).

That adds 13 to the first coordinate, and adds 0
to the second coordinate.

So altogether we have added +2-5+13 = 10 to the first coordinate, 
and added +3+7+0 = +10 to the second coordinate

So the single translation is (x,y)→(x+10,y+10)

Edwin

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SOLUTION: Name the single translation that can replace the composition of these three translations: (x,y)&#8594;(x+2,y+3), then (x,y)&#8594;(x-5,y+7), then (x,y)&#8594;(x+13,y).

SOLUTION: Name the single translation that can replace the composition of these three translations: (x,y)→(x+2,y+3), then (x,y)→(x-5,y+7), then (x,y)→(x+13,y).