What's wrong with the cartesian plane

In summary, the conversation discusses the concept of perpendicular lines in a cartesian plane. It is stated that the slope of the x-axis is 0 and the slope of the y-axis is undefined. The product of the slopes is undefined, not -1 as previously thought. The concept of limits is also brought up and it is clarified that the x-axis and y-axis are indeed perpendicular. The general condition for perpendicularity is also mentioned and it is explained that the specific conditions for the slope-product formula do not hold for the choice of the x-axis and y-axis as the two lines. Overall, the conversation provides a better understanding of the concept of perpendicular lines in a cartesian plane.
  • #1
electron
19
0
hi guyz,

im in skul and came across a small problem while solving some geometry questions

incase of cartesian plane..
slope of x-axis is tan(0)=0
and slope of y-axis is t(90)=infinite/not defined

so when we mutiply both the slopes we are suppsed to get -1
( from m(1)*m(2)= -1 ,, if m1 is 90 degrees to m2)

wat i hasd in mind is..are the x-axis and y-axis actually perpendicular..or they seem to be pependicular, i.e approaching to 90 degrees..

im sure there is some concept of limits over here...can u please tell where am i wrong..
 
Physics news on Phys.org
  • #2
The ARE perpendicular and the slope of the y-axis is undefined. So the product of the slopes is undefined, not -1. m1*m2=-1 is true only if the two lines are perpendicular and neither of them is vertical.
 
  • #3
Let us consider the general perpendicularity condition.
Given general line equations for lines passing through the origin,

Ax+By=0, Cx+Dy=0, where in each line equation, at least one of the coefficients is non-zero, these two lines are perpendicular iff AC+BD=0 (*).

In the case of non-zero coefficients, the slopes, with respect to the x-axis are:
a= -A/B and b=-C/D, respectively.

Thus, their product a*b equals (A*C)/(B*D), and inserting from (*), we get a*b=-1, under the requirement B&D different from zero.

The general condition for perpendicularity is seen to hold for the special choice of the ordinate axes as your two lines, whereas this particular choice of lines violates the specific conditions that hold for the slope-product formula.

As Dick has already told you..
 
Last edited:
  • #4
i got the point...thankx for clearing my confusion...
 

1. What is the cartesian plane and why is it important in science?

The cartesian plane, also known as the coordinate plane, is a two-dimensional graph used to plot and analyze mathematical data. It is important in science because it allows us to visually represent and understand relationships between variables and make predictions based on data.

2. How is the cartesian plane different from other coordinate systems?

The cartesian plane is different from other coordinate systems because it uses two perpendicular axes, the x-axis and y-axis, to plot points and represent data. Other coordinate systems may use different types of axes, such as polar coordinates which use radial distance and angle.

3. What limitations does the cartesian plane have?

The cartesian plane has limitations in that it can only represent two dimensions, making it difficult to visualize and analyze data with more than two variables. It also assumes a linear relationship between variables, which may not always be the case in scientific data.

4. How does the cartesian plane relate to graphing functions?

The cartesian plane is used to graph functions by plotting points on the x and y axes based on the input and output values of the function. This allows us to see the shape and behavior of the function and make predictions about its behavior.

5. Can the cartesian plane be used in fields other than math and science?

Yes, the cartesian plane can be used in various fields such as engineering, economics, and geography. It is a useful tool for representing and analyzing data in any field where relationships between variables need to be understood and visualized.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
Replies
2
Views
998
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
4K
  • Precalculus Mathematics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Precalculus Mathematics Homework Help
Replies
6
Views
2K
Back
Top