Question

1. what happens to a point (x, y) if it is reflected across the y - axis and then translated 4 units down? a. (x + 4,y - 4) b. (-x,y + 4) c. (x,y - 4) d. (-x,y - 4) 11. what does a rigid motion do to the angles of a shape? a. eliminates them b. enlarges them c. reduces them d. preserves them 12. how does a reflection affect a geometric figure? a. it mirrors it across a line b. it shrinks it c. it enlarges it d. it repositions it 13. what happens to a figure if it is rotated 360 degrees around its center of rotation? a. it looks the same as it did before rotating b. it flips over c. it disappears d. it becomes larger 14. which transformation can change the orientation of a figure to its opposite? a. reflection

Explanation:

Step1: Analyze reflection across y - axis

When a point $(x,y)$ is reflected across the y - axis, the x - coordinate changes sign. So the point becomes $(-x,y)$.

Step2: Analyze translation 4 units down

When a point is translated 4 units down, the y - coordinate decreases by 4. So the point $(-x,y)$ becomes $(-x,y - 4)$.

Step3: Answer question 11

A rigid motion (isometry) preserves the shape and size of a figure, including its angles. So the answer is that it preserves them.

Step4: Answer question 12

A reflection is a transformation that mirrors a geometric figure across a line.

Step5: Answer question 13

When a figure is rotated 360 degrees around its center of rotation, it looks the same as it did before rotating.

Answer:

1. d. $(-x,y - 4)$
2. d. Preserves them
3. a. It mirrors it across a line
4. a. It looks the same as it did before rotating