How does dilation affect the length of line segments?

Answer 1

Dilation of segment #AB# is a segment #A'B'#, where #A'# is an image of point #A# and #B'# is an image of point #B#.
The length is transformed as #|A'B'| = f*|AB|#, where #f# is a factor of dilation

Dilation or scaling is the transformation of the two-dimensional plane or three-dimensional space according to the following rules:

(a) There is a fixed point #O# on a plane or in space that is called the center of scaling.
(b) There is a real number #f!=0# that is called the factor of scaling.
(c) The transformation of any point #P# into its image #P'# is done by shifting its position along the line #OP# in such a way that the length of #OP'# equals to the length of #OP# multiplied by a factor #|f|#, that is #|OP'| = |f|*|OP|#. Since there are two candidates for point #P'# on both sides from center of scaling #O#, the position is chosen as follows: for #f>0# both #P# and #P'# are supposed to be on the same side from center #O#, otherwise, if #f<0#, they are supposed to be on opposite sides of center #O#.
It can be proven that the image of a straight line #l# is a straight line #l'#. Segment #AB# is transformed into a segment #A'B'#, where #A'# is an image of point #A# and #B'# is an image of point #B#. Dilation preserves parallelism among lines and angles between them. The length of any segment #AB# changes according to the same rule above: #|A'B'| = f*|AB|#.

The above properties and other important details about transformation of scaling can be found on Unizor

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Answer 2

Dilation affects the length of line segments by either stretching or compressing them. If the dilation factor is greater than 1, the line segment will be stretched, resulting in a longer length. Conversely, if the dilation factor is between 0 and 1, the line segment will be compressed, leading to a shorter length. However, if the dilation factor is negative, the line segment will be reflected across the line of dilation, but its length will remain the same.

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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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