Question

the center of this dilation is point (0, 0). enter a number like 5 or -5 for the value of each coordinate. (b) which of the following helps you identify the y - coordinate of the center of the dilation? a △abc and △abc are in different quadrants. b (overline{ac}) and (overline{ac}) are parallel segments. c (overline{ab}) and (overline{ab}) lie on the same line. d (overline{bc}) and (overline{bc}) both slope down to the right.

Explanation:

Step1: Recall dilation property

In a dilation centered at the origin $(0,0)$, corresponding points of the pre - image and image are collinear with the center of dilation. If two corresponding line - segments (or lines) of the pre - image and image lie on the same line, the center of dilation lies on that line. If the center of dilation is the origin, this property helps in identifying its coordinates.

Step2: Analyze options

For option A, being in different quadrants doesn't help in identifying the $y$ - coordinate of the center of dilation. For option B, parallel segments don't directly help in finding the center's $y$ - coordinate. For option C, if $\overline{AB}$ and $\overline{A'B'}$ lie on the same line, and the center of dilation is the origin $(0,0)$ (as per the first part of the problem), this property is relevant for identifying the center. For option D, the slope direction of segments doesn't help in identifying the $y$ - coordinate of the center of dilation.

Answer:

(a) 0, 0
(b) C. $\overline{AB}$ and $\overline{A'B'}$ lie on the same line.