A line segment has endpoints at #(1 ,6 )# and #(5 ,1 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Daniel L.
Nov 24, 2017

See explanation.

Explanation:

The starting points' coordinates are:

#A=(1,6)#

and

#B=(5,1)#

I step - rotate about origin.

Rotating about origin by #pi# is equal to a symetry about the origin which changes the sign of both coordinates to opposite numbers, so the new coordinates are:

#A_1=(-1,-6)#

and

#B_1=(-5,-1)#

II step - translation

Translating horizontally by #-4# means subtracting #4# from #x# coordinates.

#A_2=(-5,-6)#

and

#B_2=(-9,-1)#

II step - reflect about #Y# axis.

Reflecting about #Y# axis means changing #X# coordinate to opposite.

#A_3=(5,-6)#

and

#B_3=(9,-1)#

Finally we can say that the new coordinates are:

#A_3=(5,-6)# and #B_3=(9,-1)#

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