Parallel and Perpendicular Lines (Leaving Cert Mathematics): Flashcards

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Parallel and Perpendicular Lines
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What is true about parallel lines' slopes?

Equal slopes (m1=m2m_1 = m_2)

Angle at which perpendicular lines meet

Right angles (90°)

Product of perpendicular slopes equals

m1×m2=−1m_1 \times m_2 = -1

Slope formula for perpendicular lines

m2=−1m1m_2 = -\frac{1}{m_1}

Slope from general form ax+by+c=0ax + by + c = 0

−ab-\frac{a}{b}

First step to find parallel line equation

Find slope of given line, use same slope

First step to find perpendicular line equation

Find slope, then calculate negative reciprocal

Point-slope form equation

y−y1=m(x−x1)y - y_1 = m(x - x_1)

Negative reciprocal of ab\frac{a}{b}

−ba-\frac{b}{a}

How to verify lines are perpendicular

Multiply slopes; product should equal −1-1

What do parallel lines never do?

Never meet

Relationship between perpendicular slopes

Negative reciprocals of each other

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