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Parametric equations

  • #1

Homework Statement


Show (by eliminating the parameter) that the equations,[tex] x=x_{0}+(x_{1}-x_{0})t[/tex], [tex] y=y_{0}+(y_{1}-y_{0})t [/tex], represent the line passing through the points [tex] (x_{0},y_{0}),(x_{1},y_{1}) [/tex].


Homework Equations





The Attempt at a Solution


I get [tex]t=\frac{x-x_{0}}{x_{1}-x_{0}}=\frac{y-y_{0}}{y_{1}-y_{0}}[/tex]. And further I then get [tex]y=mx-mx_{0}+y_{0}[/tex], where, [tex] m=\frac{y_{1}-y_{0}}{x_{1}-x_{0}}[/tex]. I feel that this is not the answer to the question but if it isn't, I do not know what is? Thanks.
 

Answers and Replies

  • #2
1,341
3
Perhaps writing:

[tex]y=mx-mx_{0}+y_{0}[/tex] as [tex]y-y_0 = m(x-x_0)[/tex], [tex]m = \frac{y_1-y_0}{x_1-x_0}[/tex] rings a bell?
 
Last edited:
  • #3
I am sure it should but it is not ringing any bell with me. It is a while since I did coordinate geometry. And it got nothing to do with distance; the distance formula is [tex] \sqrt{x^2 +y^2}[/tex].
 
  • #4
374
1
You have answered the question. Review the defination of the equation of a line through two points. You will see that with a little basic algebra your expression for t= can be rewritten in the form of that defination.
 
  • #5
1,341
3
Look up point-slope form (I think that's what it's called...) and I think that you'll see it ;)
 
  • #6
Thanks for the replies.
 

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