straight lines

Question

Two lines with slopes m₁ and m₂ are perpendicular if

RankGuru · Accepted Answer

1. **Geometric Principle**: If two lines making angles $	heta_1$ and $	heta_2$ with the positive x-axis are perpendicular, then $|	heta_1 - 	heta_2| = 90^\circ$.
2. **Tangent Relation**: $	an 	heta_1 = m_1$ and $	an 	heta_2 = m_2$.
3. **Perpendicularity Condition**: For non-vertical lines, the product of their slopes must be **$-1$** ($m_1 m_2 = -1$).
4. **Meaning**: This implies one slope is the negative reciprocal of the other ($m_2 = -1/m_1$).

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