To determine which statements are true about the lines based on their equations, we need to find the slopes of each line.
The general form of a line's equation is \( y = mx + b \), where \( m \) is the slope.
The slopes from the equations provided are:
- Line A: \( y = -12x - 2 \) → slope \( m_A = -12 \)
- Line B: \( y = 2x - 3 \) → slope \( m_B = 2 \)
- Line C: \( y = 12x + 2 \) → slope \( m_C = 12 \)
- Line D: \( y = 2x + 5 \) → slope \( m_D = 2 \)
Next, to check for perpendicularity, we remember that two lines are perpendicular if the product of their slopes is -1.
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For Line A and Line C: \[ m_A \cdot m_C = (-12) \cdot 12 = -144 \quad (\text{not perpendicular}) \]
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For Line A and Line B: \[ m_A \cdot m_B = (-12) \cdot 2 = -24 \quad (\text{not perpendicular}) \]
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For Line B and Line D: \[ m_B \cdot m_D = 2 \cdot 2 = 4 \quad (\text{not perpendicular}) \]
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For Line C and Line D: \[ m_C \cdot m_D = 12 \cdot 2 = 24 \quad (\text{not perpendicular}) \]
None of the pairs of lines are perpendicular. Thus, based on the given options, none of the statements are true.
If we assume that the answer must come from one of the listed statements and acknowledge the errors in the context of this question, the analysis would indicate that all proposed statements regarding perpendicular lines are incorrect based on their slopes.
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