Perpendicular lines from equation | Mathematics I | High School Math | Khan Academy | Summary and Q&A

TL;DR

Two lines are perpendicular if they intersect at right angles and have slopes that are negative inverses of each other.

Key Insights

• 🫥 Perpendicular lines intersect at right angles and have slopes that are negative inverses of each other.
• 🫥 The product of the slopes of perpendicular lines is always equal to -1.
• 🫥 Line A and Line B are perpendicular because their slopes, 3 and -1/3, are negative inverses of each other.
• 🔙 Line C is not perpendicular to either Line A or Line B because its slope, -3, is not the negative inverse of their slopes.
• 😃 Slope-intercept form (y = mx + b) is useful for determining the slope of a line.
• 🫥 Perpendicular lines have a special relationship in geometry.
• 🫥 Understanding the concept of slope is essential when analyzing perpendicular lines.

Transcript

We are asked which of these lines are perpendicular. And it has to be perpendicular to one of the other lines, you can't be just perpendicular by yourself. And perpendicular line, just so you have a visualization for what for perpendicular lines look like, two lines are perpendicular if they intersect at right angles. So if this is one line right t... Read More

Questions & Answers

Q: What is the definition of perpendicular lines?

Perpendicular lines intersect at right angles and have slopes that are negative inverses of each other.

Q: How can you determine if two lines are perpendicular?

To determine if two lines are perpendicular, you can check if the product of their slopes is equal to -1.

Q: Can two lines with positive slopes be perpendicular?

No, two lines with positive slopes cannot be perpendicular. Perpendicular lines have slopes that are negative inverses of each other.

Q: How can you find the slope of a line in slope-intercept form?

In slope-intercept form (y = mx + b), the coefficient of x represents the slope of the line.

Summary & Key Takeaways

• Perpendicular lines intersect at right angles and have slopes that are negative inverses of each other.

• The product of the slopes of perpendicular lines is always equal to -1.

• Line A and Line B are perpendicular because their slopes, 3 and -1/3, are negative inverses of each other.