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Does the dilation pass through the center of dilation? Choose the best answer below.

(1 point)
Responses

A′B′¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is a reduction of AB¯¯¯¯¯¯¯¯
by a scale factor of 1/4
line segment cap A prime cap b prime does not pass through the center of dilation because it is a reduction of line segment cap A cap bby a scale factor of 1/4

A′B′¯¯¯¯¯¯¯¯¯¯
passes through the center of dilation because it is an enlargement of AB¯¯¯¯¯¯¯¯
by a scale factor of 4
line segment cap A prime cap b prime passes through the center of dilation because it is an enlargement of line segment cap A cap b by a scale factor of 4

A′B′¯¯¯¯¯¯¯¯¯¯
passes through the center of dilation because it is taken a line parallel to AB¯¯¯¯¯¯¯¯
line segment cap A prime cap b prime passes through the center of dilation because it is taken a line parallel to line segment cap A cap b

A′B′¯¯¯¯¯¯¯¯¯¯
does not pass through the center of dilation because it is taken a line parallel to AB¯¯¯¯¯¯¯¯
line segment cap A prime cap b prime does not pass through the center of dilation because it is taken a line parallel to line segment cap A cap b
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1 answer

To determine whether the dilation passes through the center of dilation, we need to clarify a few key concepts.

  1. Dilation: A transformation that alters the size of a figure while preserving its shape.
  2. Center of Dilation: A fixed point in a plane about which all points are expanded or contracted.

If a line segment (such as \( \overline{AB} \)) is dilated from a center of dilation \( C \) to produce a new line segment (such as \( \overline{A'B'} \)), the following holds true:

  • If the dilation is a reduction (scale factor less than 1), \( \overline{A'B'} \) does not pass through the center of dilation.
  • If the dilation is an enlargement (scale factor greater than 1), \( \overline{A'B'} \) also does not pass through the center of dilation.
  • If the line segment \( \overline{AB} \) is moved parallel to itself, then lines drawn from the center of dilation to points \( A \) and \( B \) do not create \( A' \) and \( B' \) as dilated points; hence, they do not pass through the center.

Considering these principles, the most accurate response would be:

"A′B′ does not pass through the center of dilation because it is taken a line parallel to AB."

So the best answer is:

  • A′B′ does not pass through the center of dilation because it is taken a line parallel to AB.