A square split into four separate and equal boxes shows four shapes at different scales as follows: A star at a scale of 1 to 5; an octagon at a scale of 20 to 0.5; a triangle at a scale of 10 to 1; and a pentagon at a scale of 1 to 0.1.

Question

Which scale drawing is a dilation that decreased the size of the original object it represents? Figure 1 is the star with scale 1:5
, Figure 2 is the octagon with scale 2:0.5
, Figure 3 is the triangle with scale 10:1
, and Figure 4 is the pentagon with scale 1:0.1
.

Answer 1

To determine which scale drawing represents a dilation that decreased the size of the original object, we need to analyze the scales provided for each figure.

Dilation involves scaling an object up or down. When we talk about a scale of \( a:b \), it indicates that the original object is scaled by a factor of \( \frac{a}{b} \).

• Figure 1: Star, scale 1:5

  • This means the original object (the star) has been scaled down because \( \frac{1}{5} = 0.2 \). This is a decrease in size.

• Figure 2: Octagon, scale 20:0.5

  • This means \( \frac{20}{0.5} = 40 \). This indicates a growth in size; the octagon has been scaled up.

• Figure 3: Triangle, scale 10:1

  • This means \( \frac{10}{1} = 10 \). This indicates a growth in size; the triangle has been scaled up.

• Figure 4: Pentagon, scale 1:0.1

  • This means \( \frac{1}{0.1} = 10 \). This also indicates a growth in size; the pentagon has been scaled up.

From this analysis, Figure 1, the star with a scale of 1:5, is the only figure that represents a dilation that decreased the size of the original object.