Question

Draw a figure with 3-5 sides. Label each vertex. Perform a composition transformation on your pre-image. Be sure to make note of vertex coordinates at each step. In discussion give the coordinates of your pre-image and image

Answer 1

Since I can't create visual images directly, I will guide you through the process of creating a figure with vertices, describing a transformation step-by-step, and providing the coordinates of the pre-image and image. Let's take a polygon with 4 sides (a quadrilateral) as our pre-image.

### Step 1: Draw the Quadrilateral
**Pre-image Vertices:**
1. A(1, 1)
2. B(4, 1)
3. C(4, 3)
4. D(1, 3)

### Step 2: List the Pre-image Coordinates
- A(1, 1)
- B(4, 1)
- C(4, 3)
- D(1, 3)

### Step 3: Apply a Transformation
Let's perform a composition of two transformations on the pre-image:
1. **Translation**: Move the figure 2 units to the right and 1 unit up.
2. **Rotation**: Rotate the translated figure 90 degrees counterclockwise about the origin (0, 0).

**Translation of the vertices:**
- A'(1+2, 1+1) → A'(3, 2)
- B'(4+2, 1+1) → B'(6, 2)
- C'(4+2, 3+1) → C'(6, 4)
- D'(1+2, 3+1) → D'(3, 4)

**Translated Vertices:**
- A'(3, 2)
- B'(6, 2)
- C'(6, 4)
- D'(3, 4)

### Step 4: Rotation of the Translated Vertices (90 degrees counterclockwise around the origin)
The formula for rotating a point (x, y) 90 degrees counterclockwise is (-y, x).

Applying this rotation to the translated vertices:
- A''(3, 2) → A''(-2, 3)
- B''(6, 2) → B''(-2, 6)
- C''(6, 4) → C''(-4, 6)
- D''(3, 4) → D''(-4, 3)

**Image Vertices (After Rotation):**
- A''(-2, 3)
- B''(-2, 6)
- C''(-4, 6)
- D''(-4, 3)

### Conclusion
**Coordinates of the Pre-image:**
- A(1, 1)
- B(4, 1)
- C(4, 3)
- D(1, 3)

**Coordinates of the Image:**
- A''(-2, 3)
- B''(-2, 6)
- C''(-4, 6)
- D''(-4, 3)

This sequence illustrates a composition of a translation followed by a rotation, and we've tracked the coordinates throughout the transformations.