To find the coordinates of ΔA"B"C" after the transformations, we need to apply both transformation rules step by step.
1. **Initial Coordinates:**
- \( A(-8, 4) \)
- \( B(-5, 8) \)
- \( C(-3, 3) \)
2. **First Transformation:**
The first transformation is given by the rule \((x, y) \to (x + 4, y - 6)\).
- For \( A' \):
\[
A' = (-8 + 4, 4 - 6) = (-4, -2)
\]
- For \( B' \):
\[
B' = (-5 + 4, 8 - 6) = (-1, 2)
\]
- For \( C' \):
\[
C' = (-3 + 4, 3 - 6) = (1, -3)
\]
So, the coordinates after the first transformation are:
- \( A'(-4, -2) \)
- \( B'(-1, 2) \)
- \( C'(1, -3) \)
3. **Second Transformation:**
The second transformation is given by the rule \((x, y) \to (x + 5, y - 3)\).
- For \( A'' \):
\[
A'' = (-4 + 5, -2 - 3) = (1, -5)
\]
- For \( B'' \):
\[
B'' = (-1 + 5, 2 - 3) = (4, -1)
\]
- For \( C'' \):
\[
C'' = (1 + 5, -3 - 3) = (6, -6)
\]
So, the coordinates after the second transformation are:
- \( A''(1, -5) \)
- \( B''(4, -1) \)
- \( C''(6, -6) \)
4. **Final Coordinates:**
After both transformations, the coordinates of \( \Delta A''B''C'' \) are:
- \( A''(1, -5) \)
- \( B''(4, -1) \)
- \( C''(6, -6) \)
5. **Quadrant Prediction:**
- The coordinates \( (1, -5) \), \( (4, -1) \), and \( (6, -6) \) all have positive x-coordinates and negative y-coordinates.
- This means that the points are located in the **Fourth Quadrant**.
### Summary:
The final coordinates of \( \Delta A''B''C'' \) are:
- \( A''(1, -5) \)
- \( B''(4, -1) \)
- \( C''(6, -6) \)
And the shape will be in the **Fourth Quadrant**.