Moving back and forth

Geometry Level 3

Let f f and g g be the translation of the origin to point ( 1 , 3 ) (1, 3) and point ( 4 , 1 ) (4, 1) , respectively. If g ∘ f g \circ f translates point ( 2 , 5 ) (2, 5) to point ( a , b ) (a, b) , what is a + b a+b ?


The answer is 16.

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Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

Since f : ( x , y ) → ( x + 1 , y + 3 ) f: (x, y) \rightarrow (x+1, y+3) and g : ( x , y ) → ( x + 4 , y + 1 ) g: (x, y) \rightarrow (x+4, y+1) , thus ( 2 , 5 ) → f ( 3 , 8 ) → g ( 7 , 9 ) (2, 5) \overset{f}{\rightarrow} (3, 8) \overset{g}{\rightarrow} (7, 9) . Therefore g ∘ f : ( 2 , 5 ) → ( 7 , 9 ) g \circ f: (2, 5) \rightarrow (7, 9) . Hence a + b = 7 + 9 = 16 a+b=7+9=16 .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Hi Arron, please check your answer graphically. If the translation f is applied, then the new co-ordinates of the point (2,5) must lesser in its magnitudes, that is it becomes (2-1, 5-3) and it goes on like this...

Arun M - 6 years, 2 months ago

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