1. ## Points and Vectors

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

2. Can you find the line joining those two points?

3. y = (-9/11)x + (68/11) ?

4. 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 $\ell (t) = \left( {9t - 1, - 11t + 7} \right)$.
Let $t=\frac{3}{5}$.

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

6. Originally Posted by Ari
how do we find the equation of lines in parametric form?
Consider the points $(a,b)~\&~(c,d)$.

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

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

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

8. Originally Posted by Ari
is this always true? what about if it is in R3 like my example above?
Consider the points $(x_0,y_0,z_0)~\&~(x_1,y_1,z_1)$.

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

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

In parametric form the line is $\ell (t) = \left( {(x_1-x_0)t +x_0, (y_1-y_0)t +y_0},(z_1-z_0)t +z_0 \right)$.
wow that seems pretty easy..... thanks.

10. Originally Posted by Plato
In parametric form the line is $\ell (t) = \left( {9t - 1, - 11t + 7} \right)$.
Let $t=\frac{3}{5}$.
i was thinking and is this right? i need it to be (3/5) the DISTANCE from (-1,7) to (8,-4)

11. 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?

12. 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.