Perpendicular Lines: Slope, Angle & Equations

In summary, two lines are perpendicular if and only if the product of their slopes is -1. This can be concluded by setting the product of the slopes equal to -1 and using trigonometric identities to prove it. Additionally, the slope of a line is equal to the tangent of the angle between the line and the x-axis.
  • #1
Taturana
108
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
 
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  • #2
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)
 

Related to Perpendicular Lines: Slope, Angle & Equations

1. What is the definition of perpendicular lines?

Perpendicular lines are two lines that intersect at a 90 degree angle. This means that the slope of one line is the negative reciprocal of the slope of the other line.

2. How do you find the slope of perpendicular lines?

To find the slope of perpendicular lines, take the negative reciprocal of the slope of one line. For example, if one line has a slope of 2, the perpendicular line would have a slope of -1/2.

3. Can perpendicular lines have the same slope?

No, perpendicular lines cannot have the same slope. As mentioned before, the slopes of perpendicular lines are always negative reciprocals of each other.

4. How do you write the equation of a line that is perpendicular to another line?

To write the equation of a line that is perpendicular to another line, you first need to find the slope of the original line. Then, take the negative reciprocal of that slope and plug it into the slope-intercept form of a line (y=mx+b), along with the coordinates of a point on the new line. This will give you the equation of the perpendicular line.

5. Can perpendicular lines also be parallel?

No, perpendicular lines cannot be parallel. Parallel lines never intersect, while perpendicular lines intersect at a 90 degree angle. Therefore, they cannot be both parallel and perpendicular at the same time.

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