Question

Use the function rules to find the coordinates of ДА" B" C" and predict the quadrant it will be in after the transformations. ABC, with coordinates A (-8,4), B (-5,8), and C (-3, 3), is transformed by (x, y) → (x + 4, y - 6) to produce AA' B'C". AA' B'C' is transformed by the rule (x, y) → (x + 5, y - 3). Create the rule for the composition transformation and predict what quadrant the image will be in.
(4 points) Make real short please

Answer 1

Shorter

Answer 2

To find the coordinates of points A', B', and C' after the transformations, we apply the transformation rules sequentially.

1. **First Transformation: (x, y) → (x + 4, y - 6)**
- A' = (-8 + 4, 4 - 6) = (-4, -2)
- B' = (-5 + 4, 8 - 6) = (-1, 2)
- C' = (-3 + 4, 3 - 6) = (1, -3)

2. **Second Transformation: (x, y) → (x + 5, y - 3)**
- A'' = (-4 + 5, -2 - 3) = (1, -5)
- B'' = (-1 + 5, 2 - 3) = (4, -1)
- C'' = (1 + 5, -3 - 3) = (6, -6)

**Final Coordinates:**
- A'' (1, -5)
- B'' (4, -1)
- C'' (6, -6)

**Composition Rule:**
To combine the transformations:
- Start (x, y) → (x + 4, y - 6) → (x + 9, y - 9)

**Predicted Quadrant:**
Since all final coordinates have positive x-values and negative y-values, the image will be in **Quadrant IV**.

Answer 3

1. **Transformations:**
- A → A': (-8, 4) → (-4, -2)
- B → B': (-5, 8) → (-1, 2)
- C → C': (-3, 3) → (1, -3)

- A' → A'': (-4, -2) → (1, -5)
- B' → B'': (-1, 2) → (4, -1)
- C' → C'': (1, -3) → (6, -6)

2. **Final Coordinates:**
- A'' (1, -5), B'' (4, -1), C'' (6, -6)

3. **Composition Rule:**
- Combined: (x, y) → (x + 9, y - 9)

4. **Quadrant:**
- The image is in **Quadrant IV**.