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#### Aleister911

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- Apr 6, 2021

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- Jan 30, 2018

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A straight line can be written with parametric equations $x= r_1+ tv_1$ and and $y= r_2+ tv_2$. There are many different parametric equations describing the same line. We can arbitrarily take t= 0 at $(a_1, b_1)$ and t= 1 at $(a_2, b_2)$.

you need four equations to find the values of $r_1$, $v_1$, $r_2$, and $v_2$. Those four equation are:

$a_1= r_1+ 0v_1= r_1$

$b_1= r_2+ 0v_2= r_2$

$a_2= r_1+ 1v_1= r_1+ v_1$ and

$b_2= r_2+ 1v_2= r_2+ v_2$.

From the first two equations, $r_1= a_1$ and $r_2= a_2$. The next two equations give

$a_2= r_1+ v_1= a_1+ v_1$ so $v_1= a_2- a_1$ and $b_2= r_2+ v_2= a_2+ v_2$ so $v_2= b_2- a_2$

The parametric equations for the line are

$x= a_2+ (b_1- a_1)t$

$y= a_2+ (b_2- a_2)t$

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- Apr 6, 2021

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Correct me if I'm wrong, but since we have 2 points, is it really mean that we should have two euclidean distance? if so then, can you help me solve this and optimise the distance as well?

Kind suggestion

Kind suggestion

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- #9

- Apr 6, 2021

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I'm really confused now, can you help me solve this?

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