<UserControl x:Class="MovingTheSquare.MainPage"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    mc:Ignorable="d"
    d:DesignHeight="300" d:DesignWidth="400">

    <Grid x:Name="LayoutRoot" Background="White">
        <Image Height="400" Name="image1" Stretch="None" Width="600"/>
        <TextBlock x:Name="text1" Text="Click on the square and drag it." 
            Height="25" Margin="260,-350,0,0"></TextBlock>
    </Grid>
</UserControl> 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Net;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Animation;
using System.Windows.Shapes;
using System.Windows.Media.Imaging;     // for WriteableBitmap
using System.Windows.Threading;         // for DispatcherTimer

namespace MovingTheSquare
{
    public partial class MainPage : UserControl
    {
        WriteableBitmap m_bitmap;
        DateTime m_LastUpdate;
        int x = 300, y = 200;       // initial position of the box
        int width = 600;
        int height = 400;
        int isClicked = 0;          // isClicked = 1 means being clicked
        int x_old, y_old;
        int a = 10;                 // half of the square line

        public MainPage()
        {
            InitializeComponent();

            this.MouseLeftButtonDown += new MouseButtonEventHandler(MainPage_MouseLeftButtonDown);
            this.MouseLeftButtonUp += new MouseButtonEventHandler(MainPage_MouseLeftButtonUp); 
            this.MouseMove += new MouseEventHandler(MainPage_MouseMove);
            
            m_bitmap = new WriteableBitmap(width, height);
            image1.Source = m_bitmap;

            DispatcherTimer timer = new DispatcherTimer();
            timer.Interval = new System.TimeSpan(0, 0, 0, 0, 1);
            timer.Tick += new EventHandler(timer_Tick);
            timer.Start();

            m_LastUpdate = DateTime.Now;
        }

        void timer_Tick(object sender, EventArgs e)
        {
            UpdateScene();
        }

        private void UpdateScene()
        {
            DateTime now = DateTime.Now;
            float deltaTime = (float)now.Subtract(m_LastUpdate).TotalSeconds;
            m_LastUpdate = now;

            // setting the background

            for (int i = 0; i < width * height; i++)
            {
                m_bitmap.Pixels[i] = RGBA(0,200,0,255);
            }

            DrawTheSquare(x, y);

            m_bitmap.Invalidate();
        }

        private int RGBA(byte byRed, byte byGreen, byte byBlue, byte alpha)
        {
            return (alpha * 16777216) + (byRed * 65536) + (byGreen * 256) + byBlue;
        }

        private void DrawTheSquare(int x, int y)
        {
            for (int j = (y - a); j < (y + a); j++)
            {
                for (int i = (x - a); i < (x + a); i++)
                {
                    m_bitmap.Pixels[j*width + i] = RGBA(0, 0, 200, 255);
                }
            }
        }

        private void MainPage_MouseLeftButtonDown(object sender, MouseButtonEventArgs e)
        {
            x_old = (int)(e.GetPosition(image1).X);
            y_old = (int)(e.GetPosition(image1).Y);

            if ((x - a) < x_old && x_old < (x + a))
            {
                if ((y - a) < y_old && y_old < (y + a))
                {
                    isClicked = 1;
                }
            }
        }

        private void MainPage_MouseLeftButtonUp(object sender, MouseButtonEventArgs e)
        {
            isClicked = 0;
        }

        private void MainPage_MouseMove(object sender, MouseEventArgs e)
        {
            //http://www.dotnetcurry.com/ShowArticle.aspx?ID=198

            int x_now, y_now;

            if (isClicked == 1)
            {
                x_now = (int)(e.GetPosition(image1).X);
                y_now = (int)(e.GetPosition(image1).Y);

                x += x_now - x_old;
                y += y_now - y_old;

                x_old = x_now;
                y_old = y_now;
            }
                  
        }
    }
}