Complete Question:
Katya creates handmade sets of dolls, which is sold to craft and souvenir stores. The first set of dolls has a middle diameter of 7cm and a height of 12cm.
Katya made another set of dolls. In the new set, the largest doll has a diameter of 8.75 cm and a height of 15.6 cm. Is this a dilation of the first set of dolls?
Answer:
The new set is not a dilation of the first set
Step-by-step explanation:
Given
First Set:
[tex]Height = 12cm[/tex]
[tex]Diameter = 7cm[/tex]
New Set:
[tex]Height = 15.6cm[/tex]
[tex]Diameter = 8.75cm[/tex]
Required
Determine if the new set is a dilation of the second
To do this, we pass through the following steps:
1. Divide the height of the first set by the new set
2. Divide the diameter of the first set by the new set
3. Result in (1) and (2) must be equal if the new set is a dilation of the first set
Following the steps above:
(1)
[tex]Height\ Ratio = \frac{H_2}{H_1}[/tex]
[tex]Height\ Ratio = \frac{15.6}{12}[/tex]
[tex]Height\ Ratio = 1.3[/tex]
(2)
[tex]Diameter\ Ratio = \frac{D_2}{D_1}[/tex]
[tex]Diameter\ Ratio = \frac{8.75}{7}[/tex]
[tex]Diameter\ Ratio = 1.25[/tex]
(3) Make comparison
The ratio in (1) does not equal the ratio in (2)
i.e.
[tex]1.3 \neq 1.25[/tex]
Hence, the new set is not a dilation of the first set
