is the image of

Question

under a dilation whose center is

and scale factor is


.
Triangle ABC. Point P is plotted inside Triangle ABC.




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 that Triangle A B C is inside of. Segment A prime B prime is mapped over segment A B. Segment C prime B prime is mapped over Segment B C. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one and one half. Point P is inside Triangle A B C.








A
Triangle A B C with a dilated triangle A prime B prime C prime that Triangle A B C is inside of. Segment A prime B prime is mapped over segment A B. Segment C prime B prime is mapped over Segment B C. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one and one half. Point P is inside Triangle A B C.







(Choice B) Triangle A B C with a dilated triangle A prime B prime C prime that Triangle A B C is inside of. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one and one half. Point P is inside Triangle A B C.








B
Triangle A B C with a dilated triangle A prime B prime C prime that Triangle A B C is inside of. The scale factor between triangle A prime B prime C prime and triangle A B C is between one and one and one half. Point P is inside Triangle A B C.







(Choice C) Triangle A B C with a dilated triangle A prime B prime C prime inside of it. Segment A prime B prime is mapped on segment A B. Segment C prime B prime is mapped on Segment B C. 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 inside Triangle A B C.








C
Triangle A B C with a dilated triangle A prime B prime C prime inside of it. Segment A prime B prime is mapped on segment A B. Segment C prime B prime is mapped on Segment B C. 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 inside Triangle A B C.







(Choice D) 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 inside Triangle A B C.








D
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 inside Triangle A B C.








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Answer 1

In a dilation, the image of a figure is created by scaling it from a center point. If triangle ABC needs to be dilated such that the dilated triangle A'B'C' is smaller than triangle ABC (the scale factor being between 1 and 1.5), then it implies that triangle A'B'C' lies entirely within triangle ABC.

Among the choices you provided:

• Choice A depicts triangle ABC with the dilated triangle A'B'C' that is larger than triangle ABC.
• Choice B does not specify the position of triangle A'B'C' relative to triangle ABC.
• Choice C describes a scenario where A'B'C' is indeed inside triangle ABC and mapped over segments, which aligns with the properties of a dilation.
• Choice D states that triangle A'B'C' is inside triangle ABC but lacks specifics about the segments being mapped.

Since we need a figure where triangle A'B'C' is inside triangle ABC and mapped over the specific segments mentioned (A'B' mapping over AB and C'B' mapping over BC), the best choice would be Choice C.

So, the answer is Choice C.