Use the function rules to find the coordinates of ΔA"B"C" and predict the quadrant it will be in after the transformations. ΔABC, with coordinates A(−8,4), B(−5,8), and C(−3,3), is transformed by (x,y)→(x+4,y−6) to produce ΔA′B′C′. ΔA′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)

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**.