# Equation for a line.

• Dec 7th 2007, 04:14 PM
ledbymischief
Equation for a line.
Hi. I need help finding a vector for an equation for a line. In the question i'm given 2 points which both have the same distance to the Line.

Points (2,2) and (0,-2)

I managed to find a point on the line p:(1,0) by making a vector out of the 2 given points and then dividing it by half, and so on. But i have no idea how to get the vector. Anybody who can help? Thanks a lot. Been stuck here for like the past hour. Thanks again....

Juan
• Dec 7th 2007, 05:52 PM
Plato
Try: $\displaystyle \left\langle {1, 0} \right\rangle + t\left\langle {-2,1} \right\rangle$
• Dec 8th 2007, 07:48 AM
ledbymischief
Thanks!
Thank you. But how did you get that vector? In the answer sheet it says (2,-1) but i guess its the same thing. How did you come up with (-2,1) ?? Thanks again.

Juan
• Dec 8th 2007, 08:16 AM
Plato
Well just look at $\displaystyle \left\langle {2, - 1} \right\rangle = - \left\langle { - 2,1} \right\rangle$. That means that those vectors are parallel.
So we can use either one of them or any multiple of either.

As to how I found it: I just found a vector which is perpendicular to the given vector.
• Dec 8th 2007, 08:44 AM
ledbymischief
Thanks again!
Oh yeah!! How silly i am. (ulv) = 0 makes them perpendicular to each other. Man i've forgotten so much. Thanks a bunch again!

Juan