Question

1.
Translations:
b
Translations
2.
Reflect over y-axis:
Reflect over y-axis
3.
Reflect over x-axis:
Reflect over x-axis
4.
Rotate 90 degrees clockwise:
Rotate 90 degrees clockwise
5.
Rotate 180 degrees:
Rotate 180 degrees
6.
Rotate 90 degrees counterclockwise:
Rotate 90 degrees counterclockwise
Column B
a.(-x, -y)
b.(x + a, y + b); x (+ right, - left), y (+ up, - down)
c.(-x, y)
d.(y, -x)
e.(x, -y)
f.(-y, x)

Answer 1

It looks like you're setting up a matching exercise for geometric transformations. Here’s how the transformations in Column A correspond to the transformations in Column B:

1. **Translations (b)**: **b. (x + a, y + b); x (+ right, - left), y (+ up, - down)**
This describes a translation, where you move the point by adding to the x and y coordinates.

2. **Reflect over y-axis**: **c. (-x, y)**
Reflecting a point over the y-axis changes the sign of the x-coordinate.

3. **Reflect over x-axis**: **e. (x, -y)**
Reflecting a point over the x-axis changes the sign of the y-coordinate.

4. **Rotate 90 degrees clockwise**: **f. (-y, x)**
When you rotate a point 90 degrees clockwise, the coordinates change to (-y, x).

5. **Rotate 180 degrees**: **a. (-x, -y)**
Rotating a point 180 degrees results in both coordinates changing signs.

6. **Rotate 90 degrees counterclockwise**: **d. (y, -x)**
A 90-degree counterclockwise rotation changes the coordinates to (y, -x).

Here’s the complete matching:

1. **Translations** - **b. (x + a, y + b)**
2. **Reflect over y-axis** - **c. (-x, y)**
3. **Reflect over x-axis** - **e. (x, -y)**
4. **Rotate 90 degrees clockwise** - **f. (-y, x)**
5. **Rotate 180 degrees** - **a. (-x, -y)**
6. **Rotate 90 degrees counterclockwise** - **d. (y, -x)**

Let me know if you need further help!