To determine which scale drawing represents a dilation that decreased the size of the original object, we need to look for a scale factor that is less than 1.
-
Figure 1 (star): Scale 1:5 (this is a ratio that can be interpreted as the original size being reduced to 1/5, which is a decrease).
-
Figure 2 (octagon): Scale 2:0.5 (the ratio can be interpreted as the original size being reduced to 0.5/2, which is also a decrease, but it's not as straightforward).
-
Figure 3 (triangle): Scale 10:1 (this means the size has increased; the original size is multiplied by 0.1, resulting in a decrease).
-
Figure 4 (pentagon): Scale 1:0.1 (this would indicate a significant increase, as the original size is multiplied by 10).
From this analysis:
- Figure 1 represents a decrease in size (1:5)
- Figure 2, while not immediately clear, also represents a decrease depending on the perspective of the original compared to the new
- Figure 3 also represents a decrease, but is more clearly a bigger reduction given 10:1
- Figure 4 does not represent a decrease.
Therefore, Figures 1, 2, and 3 represent a dilation that decreased the size of the original object, but Figure 1 is the simplest interpretation.
Answer: Figure 1 (star with scale 1:5) is a dilation that decreased the size of the original object.
3 answers