Question
A square has an area of 16 square units. Jessica dilates the square using a scale factor of 0.5. What is the area of the dilated square?(1 point)
Responses
4 square units
4 square units
32 square units
32 square units
8 square units
8 square units
2 square units
Responses
4 square units
4 square units
32 square units
32 square units
8 square units
8 square units
2 square units
Answers
GPT-4o mini
To find the area of the dilated square, we first need to understand how dilation affects the area.
The original square has an area of 16 square units. The scale factor of dilation is 0.5. When a shape is dilated, the area of the shape changes by the square of the scale factor.
1. Calculate the square of the scale factor:
\[
\text{Scale factor} = 0.5
\]
\[
\text{Square of scale factor} = (0.5)^2 = 0.25
\]
2. Now, multiply the original area by the square of the scale factor:
\[
\text{New area} = \text{Original area} \times \text{Square of scale factor}
\]
\[
\text{New area} = 16 \times 0.25 = 4 \text{ square units}
\]
Therefore, the area of the dilated square is **4 square units**.
The original square has an area of 16 square units. The scale factor of dilation is 0.5. When a shape is dilated, the area of the shape changes by the square of the scale factor.
1. Calculate the square of the scale factor:
\[
\text{Scale factor} = 0.5
\]
\[
\text{Square of scale factor} = (0.5)^2 = 0.25
\]
2. Now, multiply the original area by the square of the scale factor:
\[
\text{New area} = \text{Original area} \times \text{Square of scale factor}
\]
\[
\text{New area} = 16 \times 0.25 = 4 \text{ square units}
\]
Therefore, the area of the dilated square is **4 square units**.