A line segment has endpoints at #(4 ,9 )# and #(5 ,6)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-4 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Answer 1

#(-4,13)# and #(-5,10)#

In a rotation by #pi# (symmetry relatively to the origin O) #x=-x_0# and #y=-y_o# The points become #(-4,-9)# and #(-5,-6)#

A translation vertically by -4 (4 units down relatively to x-axis) means that #y=y_0-4# The points become #(-4,-13)# and #(-5,-10)#

In a reflection about the x-axis, #y=0# (symmetry relatively to the x-axis) #y=-y_o# The points become #(-4,13)# and #(-5,10)#

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Answer 2

Claire Akin

The line segment's new endpoints after the described transformations will be: Endpoint 1: (-9, -4) Endpoint 2: (-6, -7)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.