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

A dilation that decreases the size of the original object must have a scale factor of less than 1.

Let's analyze the scales provided:

1. **Figure 1: Star with scale 1:5** - This indicates that the star is being represented at 1/5th the size of the original, which is a reduction. Scale factor = 1/5 = 0.2.

2. **Figure 2: Octagon with scale 2:0.5** - This implies the octagon is represented at double its size (2) divided by half (0.5) which equals 4 (not a reduction).

3. **Figure 3: Triangle with scale 10:1** - This means the triangle is being represented at 10 times its original size (not a reduction).

4. **Figure 4: Pentagon with scale 1:0.1** - This represents the pentagon at a scale that is 1/10th of its size, which is also a reduction. Scale factor = 1/0.1 = 10 (again, not a decrease).

From this analysis, Figure 1 (the star with scale 1:5) is a dilation that decreases the size of the original object it represents.