Question

1. dilation of qrs on the coordinate plane using the origin (0, 0) as the center of dilation and a scale factor of 3 to form qrs. what statements are false? the side lengths of qrs are three times the corresponding side lengths of qrs. the angle measures of qrs are greater than the corresponding angle measures in qrs. the side lengths of qrs are ⅓ times the corresponding side lengths of qrs. the angle measures of qrs are smaller than the corresponding angle measures in qrs.

Explanation:

Step1: Recall dilation properties

In a dilation with scale - factor \(k\) centered at the origin, if the scale - factor \(k = 3\), the side - lengths of the dilated figure are \(k\) times the side - lengths of the original figure. Also, the angle measures of the dilated figure are equal to the angle measures of the original figure.

Step2: Analyze each statement

1. For the statement "The side lengths of \(Q'R'S'\) are three times the corresponding side lengths of \(QRS\)": Since the scale factor \(k = 3\), this statement is true.
2. For the statement "The angle measures of \(Q'R'S'\) are greater than the corresponding angle measures in \(QRS\)": In dilation, angle measures are preserved, so this statement is false.
3. For the statement "The side lengths of \(Q'R'S'\) are \(\frac{1}{3}\) times the corresponding side lengths of \(QRS\)": Since the scale factor is \(3\), the side - lengths of \(Q'R'S'\) are \(3\) times, not \(\frac{1}{3}\) times, the side - lengths of \(QRS\), so this statement is false.
4. For the statement "The angle measures of \(Q'R'S'\) are smaller than the corresponding angle measures in \(QRS\)": In dilation, angle measures are preserved, so this statement is false.

Answer:

The angle measures of \(Q'R'S'\) are greater than the corresponding angle measures in \(QRS\); The side lengths of \(Q'R'S'\) are \(\frac{1}{3}\) times the corresponding side lengths of \(QRS\); The angle measures of \(Q'R'S'\) are smaller than the corresponding angle measures in \(QRS\)