normal form for equation of line

[PG1995]

Hi

Could you please help me with **broken link removed** query? Thank you.


Reference: http://www.descarta2d.com/BookHTML/Chapters/lns.html


Regards
PG

 

[MrAl]

Hi,

The slope of a line 90 degrees from the radial is -1/m where m is the slope of the radial.

Another way of looking at it is if you add 90 degrees to the angle you get the angle of the 90 degree line, and the slope then would be:
m=tan(A+pi/2)=-1/tan(A)=-cot(A)

 

[steveB]

You can also use a little bit of geometry, as I've shown in the attachment.

Slope is rise over run, and I show a way to identify the rise over the run. Similar triangles can be set up to identify distance D which is the run (the run happens to be negative D here). The rise was already identified in your drawing.

Now, the triangles are obviously similar if you consider that all angles in a triangle add to 180 degrees. Then similar triangles may have different lengths for the sides, but the ratios between corresponding lengths are all equal. Hence a simple ratio identifies the length D.

 

[PG1995]

Thank you, MrAl, Steve.

A picture is worth a thousand words!

**broken link removed** is for my own reference. If you have reached here for help, then you might find **broken link removed** helpful.

Best wishes
PG

 

[MrAl]

Hi again,

We get another viewpoint from the language of vectors. Here r is the 2d vector:

r(t)=[R*cos(t),R*sin(t)]

and this is just a circle with center at the origin and the slope is just ry(t)/rx(t)=R*sin(t)/(R*cos(t)=tan(t).

The tangent vector is:
T=dr(t)/dt=r'(t)=[-R*sin(t),R*cos(t)]

and the slope of this is just ry'(t)/rx'(t)=R*cos(t)/(-R*sin(t))=-cot(t)

 

[PG1995]

Thank you, MrAl, for letting me know the alternative approach.

Is there some kind of special term to refer to **broken link removed** kind of cartesian plane where x-axis is drawn at the bottom below the negative y-axis? I have noticed that in some cases using this kind of arrangement for the axes is useful. Please let me know. Thank you.

Regards
PG

 

[MrAl]

Hi PG,

Not that i know of. It's just convenient to do it that way sometimes because that way the graduations are not sitting in the middle of the graph where they can get in the way of some plotted points.

There are many different coordinate systems however, too many perhaps
Im sure you've heard of cylindrical, spherical.