Perpendicular Lines: Slope, Angle & Equations

Click For Summary
SUMMARY

Two lines are perpendicular if the product of their slopes equals -1. Given the equations y = ax + b and g = cx + d, the condition for perpendicularity is expressed as ac = -1. The slope of a line is indeed the tangent of the angle between the line and the x-axis, confirming the relationship between slope and angle in trigonometric terms.

PREREQUISITES
  • Understanding of linear equations in the form y = mx + b
  • Basic knowledge of slopes and their geometric interpretation
  • Familiarity with trigonometric functions, particularly tangent
  • Concept of angles in relation to the Cartesian coordinate system
NEXT STEPS
  • Study the derivation of the condition for perpendicular lines in coordinate geometry
  • Explore the relationship between slopes and angles in trigonometry
  • Learn about the implications of perpendicularity in vector mathematics
  • Investigate applications of perpendicular lines in real-world scenarios, such as engineering and architecture
USEFUL FOR

Students of mathematics, geometry enthusiasts, educators teaching coordinate geometry, and anyone interested in the applications of trigonometry in understanding line relationships.

Taturana
Messages
108
Reaction score
0
A very simple and noob question, sorry for this.

Looking at http://en.wikipedia.org/wiki/Perpendicular I found that two lines are perpendicular if and only if the product of their slopes is -1.

If I have two lines described by the following equations:

y = ax + b
g = cx + d

then they're perpendicular if ac = -1 right? Okay...

What's the explanation for this? How do I conclude that they're only perpendicular if and only if the product of their slopes is -1?

Just another little question: the slope of a line is the tangent of the angle between the line and the x-axis? that's right?

Thank you
 
Mathematics news on Phys.org
HI Taturana! :smile:
Taturana said:
How do I conclude that they're only perpendicular if and only if the product of their slopes is -1?

Just another little question: the slope of a line is the tangent of the angle between the line and the x-axis? that's right?

That's right :smile: … slope = tan, and so …

tan(90º + θ) = sin(90º + θ)/cos(90º + θ) = cosθ/(-sinθ) = -1/tanθ. :wink:​

(or you can prove it just as easily by drawing it)
 

Similar threads

Undergrad Geometry problem of interest with a 3-4-5 triangle
  • · Replies 59 ·
2
Replies
59
Views
230K
MHB Find an equation of the line that is perpendicular to x - y + 2 = 0
  • · Replies 5 ·
Replies
5
Views
2K
High School How to calculate a perpendicular line?
  • · Replies 11 ·
Replies
11
Views
3K
High School Why Is the Slope Between Perpendicular Lines -1, But Not for the X and Y Axes?
  • · Replies 11 ·
Replies
11
Views
3K
High School Find line slope based on degrees (for video game programming)
  • · Replies 5 ·
Replies
5
Views
2K
High School Cross section (?) of Great Pyramid from drone footage
  • · Replies 47 ·
2
Replies
47
Views
6K
MHB How Do You Calculate the Slope of a Line with Given Coordinates and Area?
  • · Replies 2 ·
Replies
2
Views
2K
MHB What Is the Equation of a Line Parallel to 4x + 5y = 20 Passing Through (0,0)?
  • · Replies 28 ·
Replies
28
Views
5K
Undergrad Two vectors and two perpendicular lines
  • · Replies 20 ·
Replies
20
Views
2K
MHB Brie's question from Facebook (finding equation of perpendicular line)
  • · Replies 1 ·
Replies
1
Views
2K