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To determine whether lines \(AB\) and \(CD\) are parallel, perpendicular, or neither, we need to compare their slopes.

### Step 1: Calculate the slope of line \(AB\).
The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For \(A(4, 2)\) and \(B(-3, 1)\):
\[
m_{AB} = \frac{1 - 2}{-3 - 4} = \frac{-1}{-7} = \frac{1}{7}
\]

### Step 2: Calculate the slope of line \(CD\).
For \(C(-6, 0)\) and \(D(1, 1)\):
\[
m_{CD} = \frac{1 - 0}{1 - (-6)} = \frac{1}{7}
\]

### Step 3: Compare the slopes.
- If the slopes are equal, the lines are parallel.
- If the product of the slopes is \(-1\), the lines are perpendicular.

Since \(m_{AB} = \frac{1}{7}\) and \(m_{CD} = \frac{1}{7}\), the lines are **parallel**.

### Answer: **A. Parallel**

Would you like more details on the solution or have any questions?

Here are 5 related questions you can explore:
1. How can you determine if two lines are perpendicular from their slopes?
2. What is the geometric interpretation of parallel lines?
3. What does it mean for lines to be skew in three-dimensional space?
4. How would you calculate the distance between two parallel lines?
5. What happens when the slope of one line is undefined (vertical line)?

**Tip**: For lines to be perpendicular, the product of their slopes must always equal \(-1\).

Determine whether AB and CD are parallel, perpendicular, or neither. A(4,2), B(-3,1), C(-6,0), D(1,1).

Find out if lines AB and CD are parallel or perpendicular by calculating their slopes using coordinate geometry. This problem covers key concepts like slope calculation and the conditions for parallel and perpendicular lines. Suitable for Grades 9-11.

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