Question

name:
mon hw jan 26, due tuesday jan 27
project check in: check each item that is complete.
pre - image
reflection
translation
rotation
coloring

1. reflect the image over the x - axis.
2. give the rule:
3. reflect the image over the y - axis.
4. give the rule:

Explanation:

To solve the reflection problems (over the \( x \)-axis and \( y \)-axis), we use the following rules:

For Reflection over the \( x \)-axis (Problem 2):

The rule for reflecting a point \( (x, y) \) over the \( x \)-axis is:
\[ (x, y)
ightarrow (x, -y) \]
This means we keep the \( x \)-coordinate the same and negate the \( y \)-coordinate.

For Reflection over the \( y \)-axis (Problem 4):

The rule for reflecting a point \( (x, y) \) over the \( y \)-axis is:
\[ (x, y)
ightarrow (-x, y) \]
This means we negate the \( x \)-coordinate and keep the \( y \)-coordinate the same.

Example Application (Using the Triangle):

Suppose the pre - image has a vertex at \( (x, y) \):

• After reflecting over the \( x \)-axis, it becomes \( (x, -y) \).
• After reflecting over the \( y \)-axis, it becomes \( (-x, y) \).

Final Answers:

1. Rule for reflection over \( x \)-axis: \( \boldsymbol{(x, y)

ightarrow (x, -y)} \)

1. Rule for reflection over \( y \)-axis: \( \boldsymbol{(x, y)

ightarrow (-x, y)} \)

Answer:

To solve the reflection problems (over the \( x \)-axis and \( y \)-axis), we use the following rules:

For Reflection over the \( x \)-axis (Problem 2):

The rule for reflecting a point \( (x, y) \) over the \( x \)-axis is:
\[ (x, y)
ightarrow (x, -y) \]
This means we keep the \( x \)-coordinate the same and negate the \( y \)-coordinate.

For Reflection over the \( y \)-axis (Problem 4):

The rule for reflecting a point \( (x, y) \) over the \( y \)-axis is:
\[ (x, y)
ightarrow (-x, y) \]
This means we negate the \( x \)-coordinate and keep the \( y \)-coordinate the same.

Example Application (Using the Triangle):

Suppose the pre - image has a vertex at \( (x, y) \):

• After reflecting over the \( x \)-axis, it becomes \( (x, -y) \).
• After reflecting over the \( y \)-axis, it becomes \( (-x, y) \).

Final Answers:

1. Rule for reflection over \( x \)-axis: \( \boldsymbol{(x, y)

ightarrow (x, -y)} \)

1. Rule for reflection over \( y \)-axis: \( \boldsymbol{(x, y)

ightarrow (-x, y)} \)