A line segment has endpoints at #(5 ,8 )# and #(7 ,6)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #-3 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

#(5,8)to(8,-8)" and " (7,6)to(10,-6)#

Since there are 3 transformations to be performed here, name the endpoints A(5 ,8) and B(7 ,6) so we can 'track' the coordinates after each transformation.

First transformation Under a rotation about origin of #pi#

a point (x ,y) → (-x ,-y)

hence A(5 ,8) → A'(-5 ,-8) and B(7 ,6) → B'(-7 ,-6)

Second transformation Under a translation of #((-3),(0))#

a point (x ,y) → (x-3 ,y)

hence A'(-5 ,-8) → A''(-8 ,-8) and B'(-7 ,-6) → B''(-10 ,-6)

Third transformation Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-8 ,-8) → A'''(8 ,-8) and B''(-10 ,-6) → B'''(10 ,-6)

Thus after all 3 transformations.

#(5,8)to(8,-8)" and " (7,6)to(10,-6)#

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