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

1 Answer
Narad T.
Apr 30, 2017

The new end points are #(-2,-5)# and #(-4,-3)#

Explanation:

We are going to use matrices.

The matrix of rotation of #3/2pi# about the origin is

#((0,1),(-1,0))#

The matrix of reflection in the #y#-axis is

#((-1,0),(0,1))#

The combination of the 2 operations is

#((-1,0),(0,1))*((0,1),(-1,0))=((0,-1),(-1,0))#

The new end points are

#((0,-1),(-1,0))((5),(2))=((-2),(-5))#

and

#((0,-1),(-1,0))*((3),(4))=((-4),(-3))#

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