Math Is Fun Forum

bfayzah

Member

Registered: 2010-06-18

Posts: 1

Transformation/Translations, please help ; Thank you :)

The image of point (1, 0) under a reflection in point I is (17, 4). What is the image of point (16, 6) under the same translation?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Transformation/Translations, please help ; Thank you :)

Hi bfayzah

The simple translation of ( 1 , 0 ) -> ( 17, 4 ) is ( x + 16 , y + 4)

For a reflection about a point try this:

http://regentsprep.org/Regents/math/geo … /ptref.htm

Start by finding the midpoint of your two points: ( Useful for the check ).

The midpoint is ( 9 , 2 ). Now ( 1 , 0 ) -> ( 16 , 6 ) this suggests the simple translation of  (x , y) ->(x + 15, y + 6). Subjecting ( 17 , 4 ) to the negative translation of ( x - 15 , y - 6 ) yields then new point ( 2 , - 2 )

Check now by plotting the two lines (1,0)(9,2)(17,4) and (2,-2)(9,2)(16.6). Check visually for the symmetry around the midpoint. Check algebraically that all points are collinear.

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