Question

what is the result of applying a dilation with a scale factor of 3 to a rectangle with side lengths of 2 units and 4 units? a. the new rectangle has side lengths of 4 units and 8 units. b. the new rectangle has side lengths of 6 units and 12 units. c. the new rectangle has side lengths of 9 units and 18 units. d. the new rectangle has side lengths of 3 units and 6 units. what is the result of reflecting a rectangle over the x - axis and then dilating it by a scale factor of 0.75? a. the size decreases, and the figure is flipped left to right. b. the size and orientation remain unchanged. c. the size decreases, and the figure is flipped upside down. d. the size increases but the orientation remains unchanged.

Explanation:

Step1: Recall dilation formula

When dilating a figure with scale - factor $k$, the new side - length $s_{new}=k\times s_{old}$.

Step2: Solve first dilation problem

Given $k = 3$, $s_{1}=2$ and $s_{2}=4$. Then $s_{1new}=3\times2 = 6$ and $s_{2new}=3\times4 = 12$.

Step3: Recall reflection and dilation properties

Reflecting a rectangle over the x - axis flips it upside down. Dilating it with a scale factor $k = 0.75<1$ decreases its size.

Answer:

1. B. The new rectangle has side lengths of 6 units and 12 units.
2. C. The size decreases, and the figure is flipped upside down.