以下是一个基于Python的解决方案，使用了Pygame库来实现在屏幕上绘制和拖动矩形的功能：

import pygame

# 初始化Pygame
pygame.init()

# 屏幕尺寸
screen_width, screen_height = 800, 600

# 创建屏幕对象
screen = pygame.display.set_mode((screen_width, screen_height))
pygame.display.set_caption("拖动矩形示例")

# 矩形初始位置和尺寸
rect_x, rect_y = 0, 0
rect_width, rect_height = 100, 100

# 矩形选中状态
rect_selected = False

# 游戏主循环
running = True
while running:
    # 清空屏幕
    screen.fill((255, 255, 255))

    # 绘制矩形
    pygame.draw.rect(screen, (0, 0, 0), (rect_x, rect_y, rect_width, rect_height), 1)

    # 更新屏幕显示
    pygame.display.flip()

    # 处理事件
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False
        elif event.type == pygame.MOUSEBUTTONDOWN:
            # 检查鼠标是否在矩形内部
            if rect_x < event.pos[0] < rect_x + rect_width and rect_y < event.pos[1] < rect_y + rect_height:
                rect_selected = True
        elif event.type == pygame.MOUSEBUTTONUP:
            rect_selected = False
        elif event.type == pygame.MOUSEMOTION:
            if rect_selected:
                # 更新矩形位置
                rect_x += event.rel[0]
                rect_y += event.rel[1]

pygame.quit()

这段代码创建了一个窗口，然后在窗口上绘制一个空心矩形。当鼠标按下并在矩形内部移动时，矩形的位置会随之改变。当鼠标释放时，矩形停止移动。