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Determine whether the dilation is an enlargement or a reduction. (1 point) Responses AB¯¯¯¯¯¯¯¯ is an enlargement of A′B′¯¯¯¯¯¯¯¯¯¯ by a scale factor of 2. Modifying above upper A upper B with bar is an enlargement of Modifying above upper A prime upper B prime with bar by a scale factor of 2. A′B′¯¯¯¯¯¯¯¯¯¯ is an enlargement of AB¯¯¯¯¯¯¯¯ by a scale factor of 2. Modifying above upper A prime upper B prime with bar is an enlargement of Modifying above upper A upper B with bar by a scale factor of 2. A′B′¯¯¯¯¯¯¯¯¯¯ is a reduction of AB¯¯¯¯¯¯¯¯ by a scale factor of 12 . Modifying above upper A prime upper B prime with bar is a reduction of Modifying above upper A upper B with bar by a scale factor of Start Fraction 1 over 2 End Fraction . AB¯¯¯¯¯¯¯¯ is a reduction of A′B′¯¯¯¯¯¯¯¯¯¯ by a scale factor of 12 .

1 answer

To determine whether the dilation is an enlargement or a reduction, we need to examine the scale factor involved in the transformation.

  1. If the scale factor is greater than 1, it is an enlargement.
  2. If the scale factor is between 0 and 1, it is a reduction.

Now, let's look at the options:

  • AB is an enlargement of A'B' by a scale factor of 2.

    • This means if we dilate A'B' by a scale factor of 2, it becomes AB. Therefore, this statement indicates an enlargement.

  • A'B' is an enlargement of AB by a scale factor of 2.

    • This means if we dilate AB by a scale factor of 2, it becomes A'B'. This would actually suggest that A'B' is larger than AB, indicating an enlargement of AB.

  • A'B' is a reduction of AB by a scale factor of 1/2.

    • Since 1/2 is a value between 0 and 1, it indicates a reduction in size.

  • AB is a reduction of A'B' by a scale factor of 1/2.

    • This is also a reduction, confirming that AB has a smaller size than A'B'.

Considering all the statements, we have:

  • The first two statements indicate enlargements involving different segments.
  • The latter two statements indicate reductions.

Ultimately, whether the dilation is an enlargement or a reduction depends on which segment you're comparing. If AB is larger than A'B', then AB is an enlargement of A'B'. Conversely, if A'B' is larger, A'B' is an enlargement of AB. Let's clarify:

  1. Dilation of A'B' resulting in AB with a scale factor of 2 = Enlargement.
  2. Dilation of AB resulting in A'B' with a scale factor of 1/2 = Reduction.

To conclude, identify which segment is larger based on the context given (AB or A'B'). The nature of the dilation (enlargement or reduction) will depend on that comparison.