用python将（0,5）（5,5）（5,0）（7,5）4个点依次连线形成折线，将折线根据折线方向加宽1个单位，将加宽后折线延长并交于相邻折线，输出交点坐标并绘制

可以使用matplotlib库绘制折线图，使用shapely库进行折线加宽和延长并计算交点。以下是完整代码：

import matplotlib.pyplot as plt
from shapely.geometry import LineString

# 定义折线点坐标
points = [(0,5), (5,5), (5,0), (7,5)]

# 绘制原始折线
line = LineString(points)
fig, ax = plt.subplots()
x, y = line.xy
ax.plot(x, y, linewidth=2, color='blue')

# 折线加宽并绘制
width = 1
line_width = line.buffer(width, join_style=2)
x, y = line_width.exterior.xy
ax.plot(x, y, linewidth=0, color='none')
ax.fill(x, y, alpha=0.5, color='blue')

# 计算交点并绘制
intersections = []
for i in range(len(points)-1):
    seg1 = LineString([points[i], points[i+1]]).buffer(width, join_style=2)
    for j in range(i+1, len(points)-1):
        seg2 = LineString([points[j], points[j+1]]).buffer(width, join_style=2)
        inter = seg1.intersection(seg2)
        if inter.geom_type == 'MultiPoint':
            intersections += list(inter.coords)
        elif inter.geom_type == 'Point':
            intersections.append(inter.coords[0])
for pt in intersections:
    ax.plot(pt[0], pt[1], 'ro')

plt.show()

运行结果如下图所示：