How to make sure that a Point A moving in the direction V reaches at Point B?

Question

Let say I have,

Point A(X1,Y1) moving in the direction V(W, H). I need to make sure that it reaches B(X2,Y2). I think I need to subtract some value in Point A(X1, X2). But not know what? I also sure that the direction is correct.

Answer 1

You can get the displacement from A to B by subtraction. I'm not sure if your direction V is normalized or not, but if you normalize the direction and normalize the displacement vector, A will reach B if those vectors are equal.

Vector2 displacement = B - A;
displacement.Normalize();
V.Normalize();

if(displacement == V)
{
    // A will reach B if you get in here
}

Note: I'm rusty on my XNA so the specific functions you may need to call may be a little off, but the concept should work.

Post-clarification Edit:

V.Normalize();
float distance = 10.0f;  //Change this value to whatever distance you want
Point A = B - V * distance;

Answer 2

If I understand correctly, you want a point close to A such that moving from that point in the direction v will eventually reach B.

The point closest to A is the projection of A on the line (B,v). It is computed as follows:

newA = B - dot(B - A, V) / dot(V, V) * V;