A line segment has endpoints at #(3 ,7 )# and #(4 ,5)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #2 #, and reflected about the y-axis, what will the line segment's new endpoints be?

1 Answer
Narad T.
Jul 6, 2017

The new endpoints are #=(7,5)# and #=(5,6)#

Explanation:

Let the points be

#A=(3,7)# and #B=(4,5)#

The rotation about the origin by #pi/2# will transform the

#(x,y)# into #(-y,x)#

Therefore,

#A'=(-7,3)# and #B'=(-5,4)#

The vertical translation will only change the #y# coordinate

#A''=(-7,5)# and #B''=(-5,6)#

The reflection in the #y# axis will change the sign of the #x# coordinate

#A'''=(7,5)# and #B'''=(5,6)#

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