# Points and Vectors

• Jun 9th 2010, 01:02 PM
Ari
Points and Vectors
How do i find the coordinates of a point located 3/5 the distance from (-1,7) to (8,-4) ?

• Jun 9th 2010, 01:14 PM
Ackbeet
Can you find the line joining those two points?
• Jun 9th 2010, 01:56 PM
Ari
y = (-9/11)x + (68/11) ?
• Jun 9th 2010, 02:09 PM
Plato
Quote:

Originally Posted by Ari
How do i find the coordinates of a point located 3/5 the distance from (-1,7) to (8,-4) ?

In parametric form the line is $\displaystyle \ell (t) = \left( {9t - 1, - 11t + 7} \right)$.
Let $\displaystyle t=\frac{3}{5}$.
• Jun 9th 2010, 02:13 PM
Ari
Quote:

Originally Posted by Plato
In parametric form the line is $\displaystyle \ell (t) = \left( {9t - 1, - 11t + 7} \right)$.
Let $\displaystyle t=\frac{3}{5}$.

how do we find the equation of lines in parametric form? For example if i have (-1,1,5) and (6,-3,0) how do i get the equation for the line that passes through them?
• Jun 9th 2010, 02:23 PM
Plato
Quote:

Originally Posted by Ari
how do we find the equation of lines in parametric form?

Consider the points $\displaystyle (a,b)~\&~(c,d)$.

In parametric form the line is $\displaystyle \ell (t) = \left( {(c-a)t +a, (d-b)t + b} \right)$.
• Jun 9th 2010, 02:49 PM
Ari
Quote:

Originally Posted by Plato
Consider the points $\displaystyle (a,b)~\&~(c,d)$.

In parametric form the line is $\displaystyle \ell (t) = \left( {(c-a)t +a, (d-b)t + b} \right)$.

is this always true? what about if it is in R3 like (-1,1,5) and (6,-3,0) or any other two sets of numbers.
• Jun 9th 2010, 02:54 PM
Plato
Quote:

Originally Posted by Ari
is this always true? what about if it is in R3 like my example above?

Consider the points $\displaystyle (x_0,y_0,z_0)~\&~(x_1,y_1,z_1)$.

In parametric form the line is $\displaystyle \ell (t) = \left( {(x_1-x_0)t +x_0, (y_1-y_0)t +y_0},(z_1-z_0)t +z_0 \right)$.
• Jun 9th 2010, 03:00 PM
Ari
Quote:

Originally Posted by Plato
Consider the points $\displaystyle (x_0,y_0,z_0)~\&~(x_1,y_1,z_1)$.

In parametric form the line is $\displaystyle \ell (t) = \left( {(x_1-x_0)t +x_0, (y_1-y_0)t +y_0},(z_1-z_0)t +z_0 \right)$.

wow that seems pretty easy..... thanks.
• Jun 9th 2010, 04:38 PM
Ari
Quote:

Originally Posted by Plato
In parametric form the line is $\displaystyle \ell (t) = \left( {9t - 1, - 11t + 7} \right)$.
Let $\displaystyle t=\frac{3}{5}$.

i was thinking and is this right? i need it to be (3/5) the DISTANCE from (-1,7) to (8,-4)
• Jun 9th 2010, 04:48 PM
Plato
Quote:

Originally Posted by Ari
i was thinking and is this right? i need it to be (3/5) the DISTANCE from (-1,7) to (8,-4)

Why don't you try it?
Use the distance formula. You do know that, don't you?
• Jun 9th 2010, 05:56 PM
Ari
Quote:

Originally Posted by Plato
Why don't you try it?
Use the distance formula. You do know that, don't you?

lol nevermind i got it a few minutes after i posted it.