Question
Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is −34?
Drag each choice into the boxes to correctly complete the table.
A. line m, with slope 3/4
B. line n, with slope 4/3
C. line p, with slope -4/3
D. line q, with slope -3/4
Drag each choice into the boxes to correctly complete the table.
A. line m, with slope 3/4
B. line n, with slope 4/3
C. line p, with slope -4/3
D. line q, with slope -3/4
Answers
GPT-4o mini
To determine whether each line is parallel, perpendicular, or neither to a line with a slope of -34, we can use the following criteria:
1. **Parallel lines** have the same slope. Therefore, a line is parallel to the line with slope -34 if its slope is also -34.
2. **Perpendicular lines** have slopes that are negative reciprocals of each other. This means that if one line has a slope of m, a line that is perpendicular to it will have a slope of -1/m.
Now, let's analyze the slopes given for lines m, n, p, and q:
**Given slope**:
- Line with slope -34
**Slopes of other lines**:
- A. line m, with slope 3/4
- B. line n, with slope 4/3
- C. line p, with slope -4/3
- D. line q, with slope -3/4
### 1. Identify if they are parallel:
- Lines are parallel if their slopes are equal to -34. None of the slopes (3/4, 4/3, -4/3, -3/4) are equal to -34.
### 2. Identify if they are perpendicular:
To be perpendicular to -34, we calculate the negative reciprocal of -34:
\[
\text{Negative reciprocal of } -34 = \frac{1}{34}
\]
Now we check to see if any of the given slopes are equal to \( \frac{1}{34} \):
- A. \( \frac{3}{4} \) is not \( \frac{1}{34} \)
- B. \( \frac{4}{3} \) is not \( \frac{1}{34} \)
- C. \( -\frac{4}{3} \) is not \( \frac{1}{34} \)
- D. \( -\frac{3}{4} \) is not \( \frac{1}{34} \)
None of the slopes are the negative reciprocal, hence they are not perpendicular either.
### Conclusion
Since none of the lines are parallel or perpendicular to the line with a slope of -34, we can categorize them as follows:
- A. line m: Neither
- B. line n: Neither
- C. line p: Neither
- D. line q: Neither
### Summary of the table:
- **Line m:** Neither
- **Line n:** Neither
- **Line p:** Neither
- **Line q:** Neither
You may drag each line into the "Neither" category to correctly complete the table.
1. **Parallel lines** have the same slope. Therefore, a line is parallel to the line with slope -34 if its slope is also -34.
2. **Perpendicular lines** have slopes that are negative reciprocals of each other. This means that if one line has a slope of m, a line that is perpendicular to it will have a slope of -1/m.
Now, let's analyze the slopes given for lines m, n, p, and q:
**Given slope**:
- Line with slope -34
**Slopes of other lines**:
- A. line m, with slope 3/4
- B. line n, with slope 4/3
- C. line p, with slope -4/3
- D. line q, with slope -3/4
### 1. Identify if they are parallel:
- Lines are parallel if their slopes are equal to -34. None of the slopes (3/4, 4/3, -4/3, -3/4) are equal to -34.
### 2. Identify if they are perpendicular:
To be perpendicular to -34, we calculate the negative reciprocal of -34:
\[
\text{Negative reciprocal of } -34 = \frac{1}{34}
\]
Now we check to see if any of the given slopes are equal to \( \frac{1}{34} \):
- A. \( \frac{3}{4} \) is not \( \frac{1}{34} \)
- B. \( \frac{4}{3} \) is not \( \frac{1}{34} \)
- C. \( -\frac{4}{3} \) is not \( \frac{1}{34} \)
- D. \( -\frac{3}{4} \) is not \( \frac{1}{34} \)
None of the slopes are the negative reciprocal, hence they are not perpendicular either.
### Conclusion
Since none of the lines are parallel or perpendicular to the line with a slope of -34, we can categorize them as follows:
- A. line m: Neither
- B. line n: Neither
- C. line p: Neither
- D. line q: Neither
### Summary of the table:
- **Line m:** Neither
- **Line n:** Neither
- **Line p:** Neither
- **Line q:** Neither
You may drag each line into the "Neither" category to correctly complete the table.