Find coordinates point M

I need to find the coordinates of point M. Has anyone got any idea of how to find them?

Thanks in advance

[David Goodmanson]

If you put A = [Ax Ay 0], same style for B and P, then

u = cross([0 0 1],B-A);
u = u/norm(u);

is a unit vector in the direction perpendicular to the line AB. From there you should be able to construct the vector from P to M and find M.

[Jim Riggs]

This is a good idea.

Answer 1

[Jim Riggs]

See attachment.

The symbolic solution will be very messy and require quite a lot of algebra. If you have the symbolic math toolbox, Matlab can do this.

I like David Goodmanson's idea. Using his approach I get:

 Ax = ;  Ay = ;
 Bx = ;  By = ;

 k = ;  % This is a fraction (from 0 to 1) Makes sure that P lies on AB
 Px = k*(Bx-Ax);
 Py = k*(By-Ay);

 d0 = ;

 % Calculate distance from P to B
 dPB = sqrt((Bx-Px)^2+(By-Py)^2);

 Mx = Px - dPB/dPB^2*(By-Py)*d0;
 My = Py - (Bx-Px)/(By-Py)*(Mx-Px);

See the attachment (2) for the derivation.

With this approach, d0 is a signed quantity. If you set d0 to a negative value, M will be on the opposite side of line AB.

Answer 2

[help_me]

Thanks guys, you've been very helpful!

Keep up the good work! :)