3. what changes about a figure after a translation? what stays the same?
4. reflect the rhombus over the vertical line.
5. reflect the rhombus over the horizontal line.
6. what changes about a figure after a reflection? what stays the same?
7. rotate the rectangle 90 degrees clockwise.
8. rotate the rectangle 90 degrees counterclockwise.

Question

Accepted Answer

### Question 3
# Brief Explanations:
Translation is a rigid transformation (slide). The position of the figure changes (it moves to a different location). The shape, size (side lengths, angles, area, etc.), and orientation stay the same.
# Answer:
Changes: The position (location) of the figure.
Stays the same: Shape, size (side lengths, angles, area), and orientation.

### Question 6
# Brief Explanations:
Reflection is a rigid transformation (flip over a line). The orientation (left - right or top - bottom order of parts) changes (it's a mirror image). The shape, size (side lengths, angles, area), and the distance from points to the line of reflection (in a symmetric way) stay the same.
# Answer:
Changes: The orientation (it becomes a mirror - image, left - right/top - bottom order of parts may reverse).
Stays the same: Shape, size (side lengths, angles, area).

### Question 7 (Rotate rectangle 90° clockwise)
# Explanation:
## Step 1: Identify key points
Let the rectangle have vertices, say, $ A(x_1,y_1) $, $ B(x_2,y_1) $, $ C(x_2,y_2) $, $ D(x_1,y_2) $ (assuming it's axis - aligned initially, with length along x - axis and width along y - axis).
## Step 2: Apply rotation formula
The rotation formula for a point $(x,y)$ rotated 90° clockwise about the origin is $(x,y)\to(y, - x)$ (if we consider the origin as the center of rotation; if the rectangle is not at the origin, we first translate it so that the center of rotation is at the origin, rotate, then translate back). For a rectangle, after rotating 90° clockwise, the length and width swap, and the orientation changes. The new vertices will be such that the side that was horizontal becomes vertical and vice - versa.
## Step 3: Draw the rotated rectangle
Plot the new vertices. If the original rectangle has a horizontal length $ l $ and vertical width $ w $, the rotated rectangle will have horizontal width $ w $ and vertical length $ l $, with the vertices in the correct clockwise order.
# Answer:
The rectangle is rotated 90° clockwise. Its shape and size remain the same, but its orientation (the direction it is "facing") and position (if the center of rotation is not at the center of the rectangle, or relative to the coordinate system) change. The new rectangle will have its sides perpendicular to the original sides (the horizontal side becomes vertical and vice - versa).

### Question 8 (Rotate rectangle 90° counter - clockwise)
# Explanation:
## Step 1: Identify key points
Let the rectangle have vertices $ A(x_1,y_1) $, $ B(x_2,y_1) $, $ C(x_2,y_2) $, $ D(x_1,y_2) $.
## Step 2: Apply rotation formula
The rotation formula for a point $(x,y)$ rotated 90° counter - clockwise about the origin is $(x,y)\to(-y,x)$. Similar to the clockwise rotation, if the rectangle is not at the origin, we use translation - rotation - translation. For the rectangle, the length and width swap, and the orientation changes.
## Step 3: Draw the rotated rectangle
Plot the new vertices. The horizontal side of the original rectangle becomes vertical (in the opposite direction of the clockwise rotation) and the vertical side becomes horizontal.
# Answer:
The rectangle is rotated 90° counter - clockwise. Its shape and size remain the same, but its orientation and position (relative to the original or the coordinate system) change. The new rectangle will have its sides perpendicular to the original sides, with the horizontal side of the original becoming vertical (in a direction opposite to the 90° clockwise rotation) and the vertical side becoming horizontal.

### Questions 4 and 5 (Reflecting rhombus)
For Question 4 (Reflect over vertical line):
# Explanation:
## Step 1: Identify vertices of rhombus
Let the rhombus have vertices $ P, Q, R, S $.
## Step 2: Reflect each vertex
For a point $(x,y)$ reflected over a vertical line $ x = a $, the new x - coordinate is $ 2a - x $ and the y - coordinate remains the same.
## Step 3: Draw the reflected rhombus
Connect the reflected vertices. The shape and size of the rhombus stay the same, but its position (relative to the vertical line) and orientation (left - right order of vertices) change.
# Answer:
The rhombus, when reflected over the vertical line, has the same shape and size. Its position (it is a mirror image across the vertical line) and orientation (left - right arrangement of parts) change. The reflected rhombus is symmetric to the original rhombus with respect to the vertical line.

For Question 5 (Reflect over horizontal line):
# Explanation:
## Step 1: Identify vertices of rhombus
Let the rhombus have vertices $ P, Q, R, S $.
## Step 2: Reflect each vertex
For a point $(x,y)$ reflected over a horizontal line $ y = b $, the new y - coordinate is $ 2b - y $ and the x - coordinate remains the same.
## Step 3: Draw the reflected rhombus
Connect the reflected vertices. The shape and size of the rhombus stay the same, but its position (relative to the horizontal line) and orientation (top - bottom order of vertices) change.
# Answer:
The rhombus, when reflected over the horizontal line, has the same shape and size. Its position (it is a mirror image across the horizontal line) and orientation (top - bottom arrangement of parts) change. The reflected rhombus is symmetric to the original rhombus with respect to the horizontal line.

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QUESTION IMAGE

Question

Explanation:

Question 3

Step 1: Identify key points

Step 2: Apply rotation formula

Step 3: Draw the rotated rectangle

Answer:

Question 6