A line segment has endpoints at #(3 ,5 )# and #(2 ,6)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #3 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

#(3,5)to(3,8)" and " (2,6)to(2.9)#

Since there are 3 transformations to be performed, name the endpoints A(3 ,5) and B(2 ,6) so that we can 'track' the points after each transformation.

First transformation Under a rotation about origin of #pi/2#

a point (x ,y) → (-x ,y)

hence A(3 ,5) → A'(-3 ,5) and B(2 ,6) → B'(-2 ,6)

Second transformation Under a translation #((0),(3))#

a point (x ,y) → (x ,y+3)

hence A'(-3 ,5) → A''(-3 ,8) and B'(-2 ,6) → B''(-2 ,9)

Third transformation Under a reflection in the y-axis

a point (x ,y) → (-x ,y)

hence A''(-3 ,8) → A'''(3 ,8) and B''(-2 ,9) → B'''(2 ,9)

Hence after all 3 transformations.

#(3,5)to(3,8)" and " (2,6)to(2,9)#

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Answer 2

Jayden Jackson

The new endpoints of the line segment after the described transformations are:

Endpoint 1: (-5, 3) Endpoint 2: (-6, 2)

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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.