Question

Triangle A’B’C’ is a dilation of triangle ABC about point P. Triangle ABC is shown. Side AB is labeled 2 and a half. Side BC is labeled one-half. Side CA is labeled 1. Triangle ABC is is between point P and Triangle A prime B prime C prime. Side A prime B prime is labeled 7 and a half. Side B prime C prime is labeled one and a half. Side C prime A prime is labeled 3. A, enlargement B, reduction

Answer 1

Pre-Image =ΔABC

And , Image=ΔA'B'C'

Description of triangle ABC and ΔA'B'C' and Relation between them

`\rightarrow \overline{AB}=2(1)/(2)=2.5\\\\\rightarrow \overline{BC}=(1)/(2)=0.5\\\\\rightarrow \overline{AC}=1\\\\\rightarrow \overline{A'B'}=7(1)/(2)=7.5\\\\ \rightarrow \overline{B'C'}=1(1)/(2)=1.5\\\\\rightarrow \overline{A'C'}=3\\\\ \rightarrow \frac{ \overline{AB}}{ \overline{A'B'}}=(2.5)/(7.5)\\\\ \rightarrow \overline{A'B'}=3 *\overline{AB}\\\\ \rightarrow \frac{ \overline{CB}}{ \overline{C'B'}}=(0.5)/(1.5)\\\\ \rightarrow \overline{C'B'}=3 *\overline{CB}`

`\rightarrow \frac{ \overline{CA}}{ \overline{C'A'}}=(1)/(3)\\\\ \rightarrow \overline{C'A'}=3 *\overline{CA}`

⇒As, each Corresponding side of Image(ΔA'B'C') is three times the Corresponding Side of Preimage(ΔABC).

⇒So, ΔA'B'C' is Enlargement of ΔABC.

Answer 2

A. enlargement

Explanation:

A'B' has a length that is 3 times that of AB, so the dilation is an enlargement.

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The given triangles cannot exist. The short sides are too short to connect the ends of the long side.