A line segment has endpoints at #(1 ,4 )# and #(3 ,4 )#. The line segment is dilated by a factor of #6 # around #(2 ,5 )#. What are the new endpoints and length of the line segment?

Answer 1

New endpoints: #(-4,-1), (8,-1)#
New line segment length: #12#

Note that the distance between the initial line segment end points: #(1,4)# and #(3,4)# is #color(green)(2)# units.
Dilating by a factor of #color(magenta)6# will result in a new length of #color(magenta)6xxcolor(green)2=color(red)(12)#

Consider the vectors from the point of dilation: #(2,5)# and each of the end points:
#{: ("Initial endpoints:",color(white)("xxx"),(1,4),color(white)("xxx"),(3,4)), ("vector from dilation point "(2,5)":",color(white)("xxx"),(-1,-1),color(white)("xxx"),(1,-1)), ("vector after dilation " 6xx":"color(white)("xxx"),,(-6,-6),color(white)("xxx"),(6,-6)), ("new end points:",color(white)("xxx"),(2,5)+(-6,-6),color(white)("xxx"),(2,5)+(6,-6)), (,color(white)("xxx"),=color(red)(""(-4,-1)),color(white)("xxx"),=color(red)(""(8,-1))) :}#

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Answer 2

The new endpoints of the line segment after dilation are (7, 4) and (11, 4). The length of the line segment remains the same after dilation, which is 2 units.

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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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