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The problem asks for the following:

1. Plot the points \( A(-1, 2) \) and \( B(-2, -2) \).
2. Find the slope of the line \( AB \).
3. Find the slope of any line perpendicular to \( AB \).

### Step 1: Slope of line \( AB \)
The slope \( m \) between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting \( A(-1, 2) \) and \( B(-2, -2) \):
\[
m = \frac{-2 - 2}{-2 - (-1)} = \frac{-4}{-1} = 4
\]
So, the slope of line \( AB \) is \( m = 4 \).

### Step 2: Slope of a perpendicular line
The slope of a line perpendicular to another line is the negative reciprocal of the original slope. Since the slope of line \( AB \) is 4, the slope of any line perpendicular to it is:
\[
m_{\perp} = -\frac{1}{4}
\]

### Summary:
- The slope of line \( AB \) is \( 4 \).
- The slope of any line perpendicular to \( AB \) is \( -\frac{1}{4} \).

Would you like a graph of the points and lines? Feel free to ask any further clarifications.

Here are five questions related to the topic:
1. How do we determine if two lines are perpendicular just from their slopes?
2. What happens to the slope when the two points on a line are vertically aligned?
3. What is the significance of a negative reciprocal when discussing perpendicular lines?
4. How can you find the equation of a line given its slope and one point?
5. How would you extend this concept to 3D geometry?

**Tip**: When working with slopes, always pay attention to the direction of the line to avoid sign errors in slope calculation.

Plot the points and find the slope (if any) of the line they determine. Also find the common slope (if any) of the lines perpendicular to line AB. Question: A(-1,2), B(-2,-2)

This problem involves finding the slope of the line passing through points A(-1,2) and B(-2,-2), as well as determining the slope of lines perpendicular to AB. This problem explores core concepts like coordinate geometry and slopes.

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