Question
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A coordinate graph shows both the x and y axes ranging from negative 5 to 5 in unit increments. Four lines are plotted.
Find the slopes of the lines to determine which lines are perpendicular.
(1 point)
Responses
Line A is perpendicular to line C.
Line upper A is perpendicular to line upper C .
Line C is perpendicular to line D.
Line upper C is perpendicular to line upper D .
Line A is perpendicular to line D.
Line upper A is perpendicular to line upper D .
Line B is perpendicular to line C.
Line upper B is perpendicular to line upper C .
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A coordinate graph shows both the x and y axes ranging from negative 5 to 5 in unit increments. Four lines are plotted.
Find the slopes of the lines to determine which lines are perpendicular.
(1 point)
Responses
Line A is perpendicular to line C.
Line upper A is perpendicular to line upper C .
Line C is perpendicular to line D.
Line upper C is perpendicular to line upper D .
Line A is perpendicular to line D.
Line upper A is perpendicular to line upper D .
Line B is perpendicular to line C.
Line upper B is perpendicular to line upper C .
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Answers
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Answered by
GPT-4o mini
To determine which lines are perpendicular based on their slopes, we need to find the slopes of each line.
1. **Identifying the slopes**:
- The slope of a line can be calculated using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.
- If two lines are perpendicular, the product of their slopes is -1 (i.e., \( m_1 \times m_2 = -1 \)).
2. **Example calculation**:
- Suppose Line A has points (1, 2) and (2, 4). The slope \( m_A \) would be \( \frac{4 - 2}{2 - 1} = 2 \).
- For Line B, if we had points (2, 6) and (3, 4), the slope \( m_B \) would be \( \frac{4 - 6}{3 - 2} = -2 \).
3. **Finding Perpendicular Lines**:
- After calculating the slopes of each line (let's assume they are \( m_A, m_B, m_C, \) and \( m_D \)), check which pairs of slopes satisfy \( m_1 \times m_2 = -1 \).
4. **Conclusion**:
- Based on the slopes you calculated:
- If you find that \( m_A \) and \( m_C \) satisfy this condition, then Line A is perpendicular to Line C.
- Similarly, check pairs for Lines B, C, and D.
Without the specific slopes, I cannot definitively say which lines are perpendicular. However, you would check each response based on your computations:
- **Response Verification**:
- If you found that:
- Line A's slope and Line C's slope multiplied to -1, you would choose: "Line A is perpendicular to line C".
- If Line C’s slope and Line D’s slope multiplied to -1, select: "Line C is perpendicular to line D".
- And so on for Lines A and D, or B and C.
Utilize the method outlined to match the slopes and find the correct relationships.
1. **Identifying the slopes**:
- The slope of a line can be calculated using the formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.
- If two lines are perpendicular, the product of their slopes is -1 (i.e., \( m_1 \times m_2 = -1 \)).
2. **Example calculation**:
- Suppose Line A has points (1, 2) and (2, 4). The slope \( m_A \) would be \( \frac{4 - 2}{2 - 1} = 2 \).
- For Line B, if we had points (2, 6) and (3, 4), the slope \( m_B \) would be \( \frac{4 - 6}{3 - 2} = -2 \).
3. **Finding Perpendicular Lines**:
- After calculating the slopes of each line (let's assume they are \( m_A, m_B, m_C, \) and \( m_D \)), check which pairs of slopes satisfy \( m_1 \times m_2 = -1 \).
4. **Conclusion**:
- Based on the slopes you calculated:
- If you find that \( m_A \) and \( m_C \) satisfy this condition, then Line A is perpendicular to Line C.
- Similarly, check pairs for Lines B, C, and D.
Without the specific slopes, I cannot definitively say which lines are perpendicular. However, you would check each response based on your computations:
- **Response Verification**:
- If you found that:
- Line A's slope and Line C's slope multiplied to -1, you would choose: "Line A is perpendicular to line C".
- If Line C’s slope and Line D’s slope multiplied to -1, select: "Line C is perpendicular to line D".
- And so on for Lines A and D, or B and C.
Utilize the method outlined to match the slopes and find the correct relationships.
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