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is the image of


under a dilation whose center is

and scale factor is


.
Triangle ABC. Point P is plotted a distance to the right of point C.




Which figure correctly shows

using the solid line?
Choose 1 answer:
Choose 1 answer:
(Choice A) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half. Point P is to the right of point C.








A
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half. Point P is to the right of point C.







(Choice B) Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half. Point P is to the right of point C.








B
Triangle A B C with a dilated triangle A prime B prime C prime to the inside of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half. Point P is to the right of point C.







(Choice C) Triangle A B C with a dilated triangle A prime B prime C prime to the right of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half. Point P is to the right of point C prime.








C
Triangle A B C with a dilated triangle A prime B prime C prime to the right of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one half. Point P is to the right of point C prime.







(Choice D) Triangle A B C with a dilated triangle A prime B prime C prime to the right of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half. Point P is to the right of point C prime.








D
Triangle A B C with a dilated triangle A prime B prime C prime to the right of it. The scale factor between triangle A prime B prime C prime and triangle A B C is between zero and one half. Point P is to the right of point C prime.








18 of 30

1 answer

To determine the correct choice, let's analyze the details of a dilation.

  1. Dilation: In a dilation, a figure is resized around a center point based on a scale factor. If the scale factor is greater than 1, the figure enlarges, while if it is between 0 and 1, the figure shrinks.

  2. Triangle ABC and P: Since point P is plotted a distance to the right of point C, it indicates the triangles are situated in such a way that the dilated triangle is either inside or outside of triangle ABC depending on the scale factor.

Considering the choices:

  • Choice A: Describes a dilation inward (inside) with a scale factor between 1 and 0.5, which means triangle \(A'B'C'\) size is smaller than triangle ABC.

  • Choice B: Describes a dilation also inward, but with a scale factor between 0 and 0.5, which means triangle \(A'B'C'\) fits inside triangle ABC.

  • Choice C: Describes a dilation outward (to the right) with a scale factor between 1 and 0.5, meaning triangle edges are larger than triangle ABC.

  • Choice D: Describes a dilation to the right with a scale factor between 0 and 0.5, indicating triangle \(A'B'C'\) is smaller and to the right of the triangle.

Since the question suggests recognizing the scale factor and position of point P in relation to triangle ABC and its dilated image, the choices with a scale factor indicating a smaller triangle should be analyzed thoughtfully. Given that Point P is plotted to the right of point C:

  • Choices A and B (the inner dilations) don't match the outward placement of triangle \(A'B'C'\).
  • Choices C and D involve the triangle being outwards to the right, with point P also towards the right.

To find the more fitting answer based on the context of being to the right of point C:

  • If we conclude that \(P\) is to the right of both triangles, then Options C and D could be viable, but based on the scale factor context (since point P is said to be a distance to the right of C):

  • Choice C adequately illustrates that \(A'B'C'\) is larger, and thus point P is also correctly positioned relative to the setup.

Therefore, the answer that reflects the situation appropriately is likely Choice C.