Perpendicular Lines: Definition and Examples

📚 Quick Study Guide

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• Definition: Perpendicular lines are lines that intersect at a right angle (90 degrees).
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• Symbol: The symbol for perpendicularity is $ \perp $. So, line AB is perpendicular to line CD can be written as $AB \perp CD$.
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• Slope Relationship: If two non-vertical lines are perpendicular, then the product of their slopes is -1. If line 1 has slope $m_1$ and line 2 has slope $m_2$, then $m_1 * m_2 = -1$. This also means that $m_2 = - \frac{1}{m_1}$.
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• Vertical and Horizontal Lines: A vertical line and a horizontal line are always perpendicular.
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• Examples: The edges of a square or rectangle are perpendicular to each other.

Practice Quiz

1. What defines perpendicular lines?
1. Lines that are parallel.
2. Lines that intersect at any angle.
3. Lines that intersect at a 90-degree angle.
4. Lines that never meet.
2. Which of the following slope relationships indicates that two lines are perpendicular?
1. $m_1 = m_2$
2. $m_1 + m_2 = 0$
3. $m_1 * m_2 = 1$
4. $m_1 * m_2 = -1$
3. What is the slope of a line perpendicular to a line with a slope of 2?
1. 2
2. -2
3. $\frac{1}{2}$
4. $-\frac{1}{2}$
4. Which of the following pairs of lines are perpendicular?
1. y = 3x + 2 and y = 3x - 1
2. y = 2x + 5 and y = -$\frac{1}{2}$x + 3
3. y = x and y = x + 1
4. y = 4x - 2 and y = 4x + 2
5. What is the relationship between a vertical line and a horizontal line?
1. Parallel
2. Intersecting at an acute angle
3. Perpendicular
4. Skew
6. If line AB is perpendicular to line CD, how is this represented symbolically?
1. AB || CD
2. AB = CD
3. AB $ \perp $ CD
4. AB $ \angle $ CD
7. A line has the equation $y = -\frac{2}{3}x + 5$. What is the slope of a line perpendicular to it?
1. $-\frac{2}{3}$
2. $\frac{2}{3}$
3. $-\frac{3}{2}$
4. $\frac{3}{2}$