Question

1. which of the following describes the image of a figure after a dilation that has a scale factor between zero and one? a) it has a different shape from the original figure and is smaller than the original figure. b) it has the same shape as the original and is larger than the original figure. c) it has the same shape as the original and is smaller than the original figure. d) it has the same shape and same size as the original figure. 2. which of the following describes the image of a square after a dilation that has a scale factor of 6? a) its sides are 6 units longer than those of the original square. b) its sides are 1/6 as long as those of the original square. c) its sides are 6 times as long as those of the original square. d) its sides are 6 units shorter than those of the original square. 3. which of the following describes the image of a triangle after a dilation that has a scale factor of 5/6? a) each angle has 5/6 of the measure of its corresponding angle in the original triangle. b) each angle has 6/5 of the measure of its corresponding angle in the original triangle. c) each angle has the same measure as its corresponding angle in the original triangle. d) each angle is 1/6 larger than the measure of its corresponding angle in the original triangle.

Explanation:

Step1: Recall dilation properties

Dilation is a transformation that changes the size of a figure but not its shape. When the scale factor $k$ is between $0$ and $1$, the image is smaller than the original figure.

Step2: Analyze question 1

For a dilation with a scale - factor between $0$ and $1$, the image has the same shape as the original and is smaller than the original figure. So the answer to question 1 is c).

Step3: Recall dilation and side - length relationship

If the scale factor of a dilation is $k$, the lengths of the sides of the image are $k$ times the lengths of the sides of the original figure.

Step4: Analyze question 2

If the scale factor $k = 6$, the sides of the image of a square are 6 times as long as those of the original square. So the answer to question 2 is c).

Step5: Recall angle property in dilation

Dilation preserves angle measures. That is, the angles in the image have the same measure as the corresponding angles in the original figure, regardless of the scale factor.

Step6: Analyze question 3

For a dilation with a scale factor of $\frac{5}{6}$, each angle has the same measure as its corresponding angle in the original triangle. So the answer to question 3 is c).

Answer:

1. c) It has the same shape as the original and is smaller than the original figure.
2. c) Its sides are 6 times as long as those of the original square.
3. c) Each angle has the same measure as its corresponding angle in the original triangle.