Line joining the points (3,-4) and (-2,6) is perpendicular to the line joining the points (-3,6) and (9,-18).

Explanation

To determine whether the line joining the points (3, -4) and (-2, 6) is perpendicular to the line joining the points (-3, 6) and (9, -18), we need to calculate the slopes of both lines and check if their product equals -1.

### Step-by-Step Solution:

1. **Identify the Points:**
- First line: Point A (3, -4) and Point B (-2, 6)
- Second line: Point C (-3, 6) and Point D (9, -18)

2. **Calculate the Slope of the First Line (M1):**
- The formula for the slope (M) between two points (x1, y1) and (x2, y2) is:
\[ M = \frac{y2 - y1}{x2 - x1} \]
- For points A (3, -4) and B (-2, 6):
\[ M1 = \frac{6 - (-4)}{-2 - 3} = \frac{6 + 4}{-5} = \frac{10}{-5} = -2 \]

3. **Calculate the Slope of the Second Line (M2):**
- For points C (-3, 6) and D (9, -18):
\[ M2 = \frac{-18 - 6}{9 - (-3)} = \frac{-24}{12} = -2 \]

4. **Check the Relationship Between the Slopes:**
- We know that for two lines to be perpendicular, the product of their slopes must be -1:
\[ M1 \times M2 = -1 \]
- Substituting the values we found:
\[ (-2) \times (-2) = 4 \]
- Since 4 is not equal to -1, the lines are not perpendicular.

5. **Conclusion:**
- The statement that the line joining the points (3, -4) and (-2, 6) is perpendicular to the line joining the points (-3, 6) and (9, -18) is **False**.