Question

a rotation around the origin by 180 degrees changes the coordinates of a point (x, y) to _. reflecting a triangle over the x - axis will change the y - coordinates of its vertices to their _. dilations are used to resize shapes while keeping their overall _ intact.

Explanation:

Step1: Recall rotation rule

A 180 - degree rotation around the origin changes the coordinates of a point $(x,y)$ to $(-x,-y)$.

Step2: Recall reflection rule

Reflecting a point or a shape over the x - axis changes the y - coordinates of its vertices to their opposites.

Step3: Recall dilation property

Dilations are used to resize shapes while keeping their overall shape intact.

Answer:

1. $(-x,-y)$
2. Opposites
3. Shape