To determine the relationship between the two lines, we first need to find the slopes of both lines.
Step 1: Calculate the slope of line AB
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For points \( A(9, -7) \) and \( B(1, -9) \):
- \( x_1 = 9 \), \( y_1 = -7 \)
- \( x_2 = 1 \), \( y_2 = -9 \)
Now, applying the values:
\[ m_{AB} = \frac{-9 - (-7)}{1 - 9} = \frac{-9 + 7}{1 - 9} = \frac{-2}{-8} = \frac{1}{4} \]
Step 2: Calculate the slope of line CD
Next, we need the coordinates of points C and D to find the slope of line CD. Since those points weren't provided, let's denote the coordinates of points C and D as \( C(x_3, y_3) \) and \( D(x_4, y_4) \). Then, the slope \( m_{CD} \) can be calculated with:
\[ m_{CD} = \frac{y_4 - y_3}{x_4 - x_3} \]
Step 3: Compare the slopes to classify the relationship
- Parallel Lines: Two lines are parallel if their slopes are equal, i.e., \( m_{AB} = m_{CD} \).
- Perpendicular Lines: Two lines are perpendicular if the product of their slopes equals -1, i.e., \( m_{AB} \times m_{CD} = -1 \).
- Neither: If neither condition is satisfied.
Conclusion
Without specific coordinates for points C and D, we cannot definitively classify the lines. However, we have established that the slope of line AB is \( \frac{1}{4} \). If you provide the coordinates for points C and D, I can help you determine the relationship between the lines.