Matrix rotation of a rectangle to "face" a given point in 2d

Question

Suppose you have a rectangle centered at point (0, 0) and now I want to rotate it such that it is facing the point (100, 100), how would I do this purely with matrix math?

To give some more specifics I am using javascript and canvas and I may have something like this:

var position = {x : 0, y: 0 };
var destination = { x : 100, y: 100 };
var transform = Matrix.identity();

this.update = function(state) {

  // update transform to rotate to face destination

};

this.draw = function(ctx) {
  ctx.save();
  ctx.transform(transform); // a helper that just calls setTransform()      
  ctx.beginPath();
  ctx.rect(-5, -5, 10, 10);
  ctx.fillStyle = 'Blue';
  ctx.fill();
  ctx.lineWidth = 2;
  ctx.stroke();
  ctx.restore();
}

Feel free to assume any matrix function you need is available.

Answer 1

If I got my maths right in order to rotate from facing A to facing B you can use the matrix:

 [ A1*B1+A2*B2   A2*B1-A1*B2 ]
 [ A1*B2-A2*B1   A1*B1+A2*B2 ]
_______________________________

            |A|*|B|

Answer 2

Here's my first take on it:

Assuming you want the top edge of the rectangle to be the edge that sets the "facing direction" as per your comment, and that would be considered your identity direction (0, -1) or zero angle in 'JustinSpace', rotating the rect so that that edge faces 100,100 would in effect be a 135 degree rotation clockwise. Most Math libraries think of 1,0 as being the identity direction (or 0 angle) requiring a 90 deg shift of the angle to place it into 'JustinSpace'.

A matrix that rotates something 135 deg clockwise on a 2d XY plane looks like this:

float angle = Math.Atan2(100,100) + Math.Atan2(-1, 0); // 45 deg + 90 deg

//RH coordinate Row Major system
Matrix m = Matrix.Identity();
m.11 = m.22 = cos(angle);
m.12 = sin(angle);
m.21 = -sin(angle);

//for column major
//m.Transpose()

If eBusiness' answer works however, I would use it as linear algebra is almost always favorable over trig in game dev.