how to reflect an image in java

I am creating a program where I have to reflect an image horizontally and vertically. I have created a geometric shape image, but I am having a hard time figuring out how to flip my picture. I was wondering if someone could help me and tell me what to do to flip a picture. Thanks

My code so far is :

import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Color;

class DrawingDemoV3
{
    Picture canvas = null;
    Graphics g = null;
    Graphics2D g2 = null;

    DrawingDemoV3(int length, int height, Color color)
    {
        canvas = new Picture(length, height);
        canvas.setAllPixelsToAColor(color);
        g = canvas.getGraphics();
        g2 = (Graphics2D)g;
        g2.setColor(color);    
    }

    public void drawAFilledOval(Color color, int x1, int y1, int width, int height)
    {
        g2.setColor(color);
        g2.fillOval(x1, y1, width, height);
    }

    public void drawARectangle(Color color, int x1, int y1, int width, int height)
    {
        g2.setColor(color);
        g2.drawRect(x1, y1, width, height);
    }

    public void drawAFilledRectangle(Color color, int x1, int y1, int width, int height)
    {
        g2.setColor(color);
        g2.fillRect(x1,y1, width, height);
    }

    public void drawALine(Color color, int x1, int y1, int x2, int y2)
    {
        g2.setColor(color);
        g2.drawLine(x1,y1,x2,y2);
    }

    public Picture getDrawing()
    {
        return canvas;
    }
}

public class DrawingDemoTesterV3
{
    public static void main(String[] args)
    {
        DrawingDemoV3 drawing1 = new DrawingDemoV3(200, 200, Color.BLACK);   

        drawing1.drawAFilledRectangle(Color.PINK, 90, 0, 20, 200);
        drawing1.drawAFilledRectangle(Color.PINK, 0, 90, 200, 20);
        drawing1.drawARectangle(Color.CYAN, 40, 40, 120, 120);
        drawing1.drawALine(Color.ORANGE, 0,0, 200, 200);
        drawing1.drawALine(Color.ORANGE, 200,0, 0, 200);
        drawing1.drawAFilledOval(Color.YELLOW, 80, 80, 38, 36);

        Picture picture1 = drawing1.getDrawing();
        picture1.show();
    }
}