A line segment has endpoints at #(5 , 2)# and #(3 , 1)#. 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
May 24, 2018

Answer:

#color(blue)((-2,-7)#

#color(blue)((-1,-5)#

Explanation:

No direction of rotation is given, so I will take this as anti-clockwise:

A rotation of #pi/2# anti-clockwise maps:

#(x,y)->(y,-x)#

A translation of -2 units map:

#(x,y)->(x,y-2)#

A reflection in the y axis map:

#(x,y)->(-x,y)#

If we combine these, we get:

#(x,y)->(y,-x)->(y,-x-2)->(-y,-x-2)#

Therefore:

#(5,2)->(-y,-x-2)=(-2,-7)#

#(3,1)->(-y,-x-2)=(-1,-5)#