Perpendicular Lines D36Db8

1. **Problem Statement:** We want to understand what perpendicular lines are and how to identify them. 2. **Definition:** Two lines are perpendicular if they intersect at a right angle, which is $90^\circ$. 3. **Slope Relationship:** If the slope of one line is $m_1$ and the slope of another line is $m_2$, then the lines are perpendicular if and only if: $$m_1 \times m_2 = -1$$ This means the slopes are negative reciprocals of each other. 4. **Example:** Suppose one line has slope $2$. The line perpendicular to it will have slope: $$m_2 = -\frac{1}{2}$$ 5. **Why this works:** The product of the slopes being $-1$ ensures the angle between the lines is $90^\circ$. 6. **Summary:** To check if two lines are perpendicular, multiply their slopes. If the product is $-1$, the lines are perpendicular. This is a fundamental concept in geometry and algebra related to lines on the coordinate plane.