Question

Line n and points A through E are shown in the coordinate plane below.

5
a
D
A
с
E
5
Ayako claims that there are centers of dilations through which a dilation of line n by a factor of 1.5 leaves
Line n unchanged. Determine whether each point below represents a center of dilation that supports
Ayako's claim. Select Yes or No for each point.
Yes No
Point AOC
Point BOO
Point COO
Point DOO
Point EOC

Answer 1

The points that represent a center of dilation that supports Ayako's claim are;

Point A; Yes

Point D; Yes

Explanation:

When the figure being dilated has a segment or side that rests on the center of dilation, the corresponding side or segment of the image of the preimage of the figure will both be located on the same line

Therefore, given that the line 'n' is infinite, the centers of dilation through which a dilation of the line 'n' will form an image that will be on the same line as line 'n' are centers of dilation located on line 'n', which are;

Point A and Point D