[hardwired]

There are two general ways to do this:
1 — drawing the images in a JPanel
2 — mounting scaled images in JLabels.
Here's an example showing both ways:

Code:

import java.awt.*;
import java.awt.event.*;
import java.awt.geom.AffineTransform;
import java.awt.image.BufferedImage;
import java.io.*;
import java.util.Hashtable;
import javax.imageio.ImageIO;
import javax.swing.*;
import javax.swing.event.*;

public class MultiScale implements ChangeListener {
    BufferedImage[] images;
    ImageScalePanel imagePanel;
    JLabel[] labels;
    double scale = 1.0;

    public MultiScale(BufferedImage[] images) {
        this.images = images;
    }

    public void stateChanged(ChangeEvent e) {
        int value = ((JSlider)e.getSource()).getValue();
        scale = (value+4)/20.0;
        imagePanel.setScale(scale);
        setImages();
    }

    private JPanel getContent() {
        imagePanel = new ImageScalePanel(images);
        imagePanel.setBorder(BorderFactory.createTitledBorder("graphic"));
        JPanel panel = new JPanel(new GridBagLayout());
        GridBagConstraints gbc = new GridBagConstraints();
        gbc.weighty = 1.0;
        gbc.gridwidth = GridBagConstraints.REMAINDER;
        panel.add(imagePanel, gbc);
        panel.add(getLabelPanel(), gbc);
        return panel;
    }

    private JPanel getLabelPanel() {
        JPanel panel = new JPanel(new GridLayout(1,0));
        panel.setBorder(BorderFactory.createTitledBorder("labels"));
        labels = new JLabel[3];
        for(int i = 0; i < labels.length; i++) {
            labels[i] = new JLabel((ImageIcon)null, JLabel.CENTER);
            panel.add(labels[i]);
        }
        setImages();
        return panel;
    }

    private void setImages() {
        for(int i = 0; i < labels.length; i++) {
            labels[i].setIcon(new ImageIcon(getScaledImage(i)));
        }
        labels[0].getParent().validate();
    }

    private BufferedImage getScaledImage(int index) {
        int w = (int)(scale*images[index].getWidth());
        int h = (int)(scale*images[index].getHeight());
        int type = images[index].getType();
        BufferedImage image = new BufferedImage(w, h, type);
        Graphics2D g2 = image.createGraphics();
        g2.setRenderingHint(RenderingHints.KEY_INTERPOLATION,
                            RenderingHints.VALUE_INTERPOLATION_BICUBIC);
        g2.drawImage(images[index], 0, 0, w, h, labels[index]);
        g2.dispose();
        return image;
    }

    private JSlider getSlider() {
        int min = 1, max = 36, inc = 5;
        JSlider slider = new JSlider(min, max, 16);
        slider.setMajorTickSpacing(5);
        slider.setMinorTickSpacing(1);
        slider.setPaintTicks(true);
        slider.setSnapToTicks(true);
        slider.setLabelTable(getLabelTable(min, max, inc));
        slider.setPaintLabels(true);
        slider.addChangeListener(this);
        return slider;
    }

    private Hashtable getLabelTable(int min, int max, int inc) {
        Hashtable<Integer,JLabel> table = new Hashtable<Integer,JLabel>();
        for(int j = min; j <= max; j += inc) {
            String s = String.format("%.2f", (j+4)/20.0);
            table.put(Integer.valueOf(j), new JLabel(s));
        }
        return table;
    }

    public static void main(String[] args) throws IOException {
        String prefix = "images/geek/geek";
        String ext = ".gif";
        String[] ids = { "-c---", "--g--", "---h-" };
        BufferedImage[] images = new BufferedImage[ids.length];
        for(int i = 0; i < images.length; i++) {
            String path = prefix + ids[i] + ext;
            images[i] = ImageIO.read(new File(path));
        }
        MultiScale test = new MultiScale(images);
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.getContentPane().add(new JScrollPane(test.getContent()));
        f.getContentPane().add(test.getSlider(), "Last");
        f.setSize(400,400);
        f.setLocation(200,200);
        f.setVisible(true);
    }
}

class ImageScalePanel extends JPanel {
    BufferedImage[] images;
    double scale = 1.0;
    int totalWidth;

    public ImageScalePanel(BufferedImage[] images) {
        this.images = images;
        for(int i = 0; i < images.length; i++)
            totalWidth += images[i].getWidth();
    }

    public void setScale(double scale) {
        this.scale = scale;
        revalidate();
        repaint();
    }

    protected void paintComponent(Graphics g) {
        super.paintComponent(g);
        Graphics2D g2 = (Graphics2D)g;
        g2.setRenderingHint(RenderingHints.KEY_INTERPOLATION,
                            RenderingHints.VALUE_INTERPOLATION_BICUBIC);
        double x = getInsets().left;
        double y = getInsets().top;
        for(int i = 0; i < images.length; i++) {
            AffineTransform at = AffineTransform.getTranslateInstance(x,y);
            at.scale(scale, scale);
            g2.drawRenderedImage(images[i], at);
            x += scale*images[i].getWidth();
        }
    }

    public Dimension getPreferredSize() {
        Insets insets = getInsets();
        int vi = insets.top + insets.bottom;
        int hi = insets.left + insets.right;
        int w = (int)(scale*totalWidth) + hi;
        int h = (int)(scale*images[0].getHeight()) + vi;
        return new Dimension(w, h);
    }
}

Images from Using Swing Components Examples, down low.