The distance between a line and a point

[seto6]

Homework Statement

So this it the problem, i am not so good at latex, so i decided to use MS office:

Homework Equations

the cross product?

The Attempt at a Solution

ok i tried this but i got stuck, because i got the bottom right, i am not sure if the top is correct, what if the line (A) does not pass through the origin, then my method won't work, pointing me in the correct direction would be helpfull, also how do you get the projections of V on d, i know how to get the projection of V on A.

 

[hunt_mat]

I presume that this is the shortest distance from the point (x_{1},y_{1}) to the line? This happens when you look at the normal to the line passing through the point (x_{1},y_{1}) which you have noted.

Can you write the line in vector form? If two vectors are perpendicular to each other, what is the value of their dot product? Can you construct the normal from this?

Mat

 

[seto6]

the vector i am trying to find is d, which is perpendicular to A, thus if i do a dot product i would get a zero, but i won't be able to find d.

 

[hunt_mat]

I would instingtively use co-ordainate geometry. The cross product only makes sense for three dimensional vectors.
Write \mathbf{d}=a\mathbf{i}+b\mathbf{j} and then by taking the dot product with the vector representing the line you will be able to find either a or b and use that to find the vector d.