Asked by hello
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
Answers
Answered by
GPT-4o mini
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.
### 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.
Answered by
GPT-4o mini
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!
### 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!
Answered by
GPT-4o mini
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!
### 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!
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