one lines passes through points A and B (9,-7) (1,-9). Another line passes through points C and D. Classify the lines as parallel, perpendicular or neither

5 answers

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.

could you make it a little more clearer without the symbols

Sure! Let's break it down step by step in simpler terms without using symbols.

Step 1: Find the slope of line AB

To find the slope of the line that passes through points A (9, -7) and B (1, -9), we use the following steps:

  1. Subtract the y-coordinates: Take the y-coordinate of point B and subtract the y-coordinate of point A: \[ -9 - (-7) = -9 + 7 = -2 \]

  2. Subtract the x-coordinates: Do the same with the x-coordinates: \[ 1 - 9 = -8 \]

  3. Calculate the slope: Now, divide the result from step 1 by the result from step 2: \[ \text{slope of line AB} = \frac{-2}{-8} = \frac{1}{4} \]

Step 2: Find the slope of line CD

For the second line, which passes through points C and D, we need the coordinates of those points to calculate the slope in the same way.

  1. Assuming you have points C and D, you subtract the y-coordinates of C and D and the x-coordinates of C and D.

  2. Calculate the slope for line CD using the same method as above.

Step 3: Compare the slopes

Once you have the slope of line CD:

  1. Determine if they are parallel: If the slope of line AB (which is 1/4) is equal to the slope of line CD, then the lines are parallel.

  2. Determine if they are perpendicular: If the product of the slopes equals -1 (this means if you multiply the slope of line AB by the slope of line CD and get -1), then the lines are perpendicular.

  3. If neither condition is satisfied, then the lines are neither parallel nor perpendicular.

Conclusion

Right now, we know that the slope of line AB is 1/4. If you provide the coordinates of points C and D, I can help you find the slope of line CD and classify the relationship between the two lines!

sorry forgot to add the coordinates to C and D (5,-3) (-3,-5)

No problem! Now that we have the coordinates for points C and D, let's find the slope of line CD and then compare it to the slope of line AB.

Step 1: Find the slope of line CD

Line CD passes through points C (5, -3) and D (-3, -5). We'll calculate the slope using the same method we used before:

  1. Subtract the y-coordinates: Take the y-coordinate of point D and subtract the y-coordinate of point C: \[ -5 - (-3) = -5 + 3 = -2 \]

  2. Subtract the x-coordinates: Now, take the x-coordinate of point D and subtract the x-coordinate of point C: \[ -3 - 5 = -8 \]

  3. Calculate the slope: Divide the result from step 1 by the result from step 2: \[ \text{slope of line CD} = \frac{-2}{-8} = \frac{1}{4} \]

Step 2: Compare the slopes

Now we have the slope of both lines:

  • The slope of line AB (from points A and B) is \( \frac{1}{4} \).
  • The slope of line CD (from points C and D) is also \( \frac{1}{4} \).

Conclusion

Since both lines have the same slope of \( \frac{1}{4} \), this means that lines AB and CD are parallel.

If you have any more questions or need further assistance, feel free to ask!