Finding coordinate of the line?

Question

Here is my code. Here I make some drawing and transformation.
I have problem finding the coordinate of the line after I have done some transformation on it.
How should I code it so the program will let me know the start and end coordinate of the line once it's translated?
In this case, I want to find the coordinate "d". Coordinate a, b and c are given. (Pliz compile and run to be clear with it).
Thanks.
Chevas.
import java.awt.*;
import java.awt.geom.*;
import javax.swing.JComponent;
import javax.swing.JFrame;
public class TransformTranslatedRotation extends JComponent {
     public void paint(Graphics g) {
          double a[] = {50,90};
          double b[] = {150,70};
          double c[] = new double[2];
          double d[] = new double[2];
          c[0]= (a[0]+b[0])/2;
          c[1]= (a[1]+b[1])/2;
          System.out.println("a (" + a[0] + " , " + a[1] +")");
          System.out.println("b (" + b[0] + " , " + b[1] +")");
          System.out.println("c (" + c[0] + " , " + c[1] +")");
          Point2D.Double a1 = new Point2D.Double(a[0], a[1]);
          Point2D.Double b1 = new Point2D.Double(b[0], b[1]);
          Point2D.Double c1 = new Point2D.Double(c[0], c[1]);
          Point2D.Double d1 = new Point2D.Double();
          double dist_ab = a1.distance(b1);
          System.out.println("distance ab: " + dist_ab);
         Graphics2D g2 = (Graphics2D) g;
         g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
         g2.setPaint(Color.black);        
          g2.drawLine((int)a[0], (int)a[1], (int)b[0], (int)b[1]);
          g2.drawString("a", (int)a[0]-5, (int)a[1]-5);
          g2.drawString("b", (int)b[0]-5, (int)b[1]-5);
          g2.drawString("c", (int)c[0]-5, (int)c[1]-5);
          g2.drawString("d", (int)c[0]+15, (int)(c[1]*2.5));
         AffineTransform rat1 = new AffineTransform();
          System.out.println("tx: " + rat1.getTranslateX());
          System.out.println("ty: " + rat1.getTranslateY());
         rat1.rotate(Math.PI/2, c[0], c[1]);
         rat1.translate(c[0]-a[0],c[1]-a[1]);
         g2.transform(rat1);
         g2.drawLine((int)a[0], (int)a[1], (int)b[0], (int)b[1]);
          System.out.println("tx: " + rat1.getTranslateX());
          System.out.println("ty: " + rat1.getTranslateY());
     public static void main(String[] a) {
         JFrame f = new JFrame();
         f.getContentPane().add(new TransformTranslatedRotation());
         f.setSize(400, 300);
         f.show();
}

Answer 1

tx = Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.
ty = Returns the X coordinate of the translation element (m12) of the 3x3 affine transformation matrix.