A line segment has endpoints at #(3 ,8 )# and #(4 ,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

#(8,6)" and " (6,7)#

Since there are 3 transformations to be performed here, label the endpoints A(3 ,8) and B(4 ,6)

First transformation Under a rotation about the origin of #pi/2#
#"a point " (x,y)to(-y,x)#

Hence A(3 ,8)→ A'(-8 ,3) and B(4 ,6) → B'(-6 ,4)

Second transformation Under a translation #((0),(3))#
#"a point " (x,y)to(x,y+3)#

Hence A'(-8 ,3) → A''(-8 ,6) and B'(-6 ,4) → B''(-6 ,7)

Third transformation Under a reflection in the y-axis

#"a point " (x,y)to(-x,y)#

Hence A''(-8 ,6) → A'''(8 ,6) and B''(-6 ,7) → B'''(6 ,7)

After all 3 transformations.

#(3,8)to(8,6)" and " (4,6)to(6,7)#
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Answer 2

The new endpoints of the line segment will be (-8, 3) and (-6, 4).

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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.

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.

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.

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.

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