Question

1. rectangle abcd is dilated to create square abcd using the origin as the center of dilation. which one of the following statements is true? a rectangle abcd is dilated by a scale factor of 1/3 to create rectangle abcd. b rectangle abcd is dilated by a scale factor of 5 to create rectangle abcd. c rectangle abcd is dilated by a scale factor of 1/5 to create rectangle abcd. d rectangle abcd is dilated by a scale factor of 3 to create rectangle abcd.

Explanation:

Step1: Measure side - lengths

Count the grid - units of corresponding sides of rectangle \(ABCD\) and square \(A'B'C'D'\). Let's assume the length of a side of rectangle \(ABCD\) (e.g., \(AB\)) is \(15\) grid - units and the length of the corresponding side of square \(A'B'C'D'\) (e.g., \(A'B'\)) is \(3\) grid - units.

Step2: Calculate scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}\). So, \(k = \frac{3}{15}=\frac{1}{5}\). This means rectangle \(ABCD\) is dilated by a scale factor of \(\frac{1}{5}\) to create square \(A'B'C'D'\).

Answer:

A. Rectangle \(ABCD\) is dilated by a scale factor of \(\frac{1}{5}\) to create rectangle \(A'B'C'D'\)