Given:
Two similar figures.
Solution:
Part a:
ΔABC and ΔA'B'C' are similar.
Similarity statement:
If two triangles are similar, then the corresponding sides are in proportion.
[tex]$\frac{A B}{A^{\prime} B^{\prime}} = \frac{6}{24} =\frac{1}{4}[/tex]
[tex]$\frac{BC}{B^{\prime} C^{\prime}} = \frac{12}{48} =\frac{1}{4}[/tex]
[tex]$\frac{CA}{C^{\prime} A^{\prime}} = \frac{15}{60} =\frac{1}{4}[/tex]
The sides are in the same ratio. Therefore the two triangles are similar.
Part b:
The sides of A'B'C' are greater than the original image ABC.
Therefore, the dilation A'B'C' is an enlargement.
Part c:
Scale factor:
[tex]$K =\frac{\text {Side length of image }}{\text {Side length of original }}[/tex]
[tex]$K =\frac{A^{\prime}B^{\prime}}{AB}[/tex]
[tex]$K =\frac{24}{6}[/tex]
K = 4
Scale factor = 4
K > 1
Therefore the image of the dilation is enlargement.
