Question

Y'Z' has endpoints located at Y(0, 3) and 2-6, 3). YZ was dilated at a scale factor of 3 from the origin. Which statement describes the pre-image?

O
is located at Y (0, 9) and Z (-18, 9) and is three times the size of y
O
YZ is located at Y (0, 3) and Z (-6, 3) and is the same size as y'z
OYZ is located at Y (0, 1.5) and Z (-3, 1.5) and is the one-half the size of y'z
OYZ is located at Y (0, 1) and Z (-2, 1) and is one-third the size of yz

Answer 1

The correct statement is:

`\[ YZ \text{ is located at } Y(0, 1) \text{ and } Z(-2, 1) \text{ and is one-third the size of } Y'Z' \]`

The pre-image YZ, which is dilated at a scale factor of 3 from the origin, experiences a transformation. The original points Y(0, 3) and Z(-6, 3) are dilated by a factor of 3, resulting in the new coordinates Y(0, 1) and Z(-2, 1). Therefore, the correct statement is that YZ is located at Y(0, 1) and Z(-2, 1) and is one-third the size of the original Y'Z'.

The dilation process involves stretching or shrinking a figure while maintaining its shape and orientation. In this case, the scale factor of 3 indicates an enlargement, making YZ three times larger than its pre-image Y'Z'. The coordinates of Y and Z are adjusted accordingly, with the y-coordinates being divided by 3.

To clarify, the other options are incorrect. YZ is not three times the size of Y'Z', nor is it the same size as Y'Z'. Additionally, YZ is not one-half the size of Y'Z', nor is it located at Y(0, 1.5) and Z(-3, 1.5). The accurate description reflects the dilation from the origin, resulting in YZ at Y(0, 1) and Z(-2, 1), with a scale factor of one-third compared to Y'Z'.