1. ## Parametric Equations II

Find parametric equations to describe the line 3x + 4y = 12. Use your equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).

I can find the parametric equations to describe the line 3x + 4y = 12. I am having trouble using the equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).

2. Originally Posted by thamathkid1729
Find parametric equations to describe the line 3x + 4y = 12. Use your equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).

I can find the parametric equations to describe the line 3x + 4y = 12. I am having trouble using the equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3).

$\displaystyle x=4 \lambda$

$\displaystyle y=3(1-\lambda)$ ?

If so the required point is obtained by setting $\displaystyle \lambda=2/5$

CB

3. What Captain Black did was find parametric equations such that $\displaystyle \lambda= 0$ at the point (0, 3) and $\displaystyle \lambda= 1$ at the point (4, 0). "Three fifths of the way from (4, 0) to (0, 3)" is 1- 3/5= 2/5 of the way from (0, 3) to (4, 0).

I think I would have been inclined to do it the other way: find parametric equations such that $\displaystyle \lambda= 0$ gives the point (4, 0), and $\displaystyle \lambda= 1$ gives the point (0, 3). That way, "three fifths of the way from (4, 0) to (0, 3)" would be simply $\displaystyle \lambda= 3/5$. Of course, to do that you would use the vector <0- 4, 3- 0>= <-4, 3> as the "direction vector".

Thamathkid1729, what parametric equations did you get?

4. The parametric equations I found were:

x = -4 + 4t
y = 6 - 3t

I just found arbitrary parametric equations... Can I still use these equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3)?

5. Originally Posted by thamathkid1729
The parametric equations I found were:

x = -4 + 4t
y = 6 - 3t

I just found arbitrary parametric equations... Can I still use these equations to find coordinates for the point that is three-fifths of the way from (4, 0) to (0, 3)?
Yes, first find the value of $\displaystyle $$t_1 that corresponds to \displaystyle (4,0) and then the value of \displaystyle$$t_2$ that corresponds to $\displaystyle (0,3)$.

Then the parameter value corresponding to the required point is:

$\displaystyle t_3=t_1+\frac{3}{5}(t_2-t_1)$

CB