Verifying Lines are Perpendicular

AI Thread Summary
To verify if the lines L: x - 2y + 3 = 0 and K: 2x + y = 0 are perpendicular, convert both equations to slope-intercept form (y = mx + b). The slopes of the lines can then be compared; if they are opposite reciprocals, the lines are perpendicular. The discussion emphasizes that the verification process is straightforward and primarily involves checking the slopes. There is a mention of a potential confusion regarding the factor of 3 from line L, but the main focus remains on the slope comparison. Understanding the relationship between the slopes is key to confirming perpendicularity.
odolwa99
Messages
85
Reaction score
0
Just a quick question here. Have I done this correctly? Do I need to factor in the 3 from L?

Many thanks.

Homework Statement



Q. Verify that the lines L: x -2y + 3 = 0 & K: 2x + y = 0 are perpendicular.

Homework Equations



The Attempt at a Solution



x(x) + y(y) = 0 => 1(2) + (-2)(1) = 2 - 2 = 0.
 
Physics news on Phys.org
I have no idea what your solution is supposed to show, but verifying that two lines are perpendicular is easy. Just put them in y=mx+b form and compare them. If their slopes are opposite and reciprocal (2/3, -3/2 for example), then they are perpendicular.
 
Ok, thank you.
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
Back
Top