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) 32 square units 2 square units 8 square units 4 square units

Explanation:

Step1: Find side length of original square

The area of a square is given by \( A = s^2 \), where \( s \) is the side length. For the original square with area \( 16 \) square units, we solve \( s^2 = 16 \). Taking the square root of both sides, \( s=\sqrt{16} = 4 \) units.

Step2: Find side length of dilated square

The scale factor of dilation is \( 0.5 \). To find the side length of the dilated square, we multiply the original side length by the scale factor: \( s_{\text{dilated}}=4\times0.5 = 2 \) units.

Step3: Find area of dilated square

Using the area formula for a square again, with the new side length \( s_{\text{dilated}} = 2 \) units, the area \( A_{\text{dilated}}=(2)^2=4 \) square units. Alternatively, we can use the property that when a figure is dilated by a scale factor \( k \), the area is scaled by \( k^2 \). Here, \( k = 0.5 \), so the area scale factor is \( (0.5)^2=0.25 \). Then, the area of the dilated square is \( 16\times0.25 = 4 \) square units.

Answer:

4 square units (corresponding to the option: 4 square units)