用python将（0,5）（5,5）（5,0）（7,5）4个点依次连线形成折线，将折线沿折线方向加宽为2个单位，然后将加宽后折线延长并交于相邻折线，最后输出交点坐标并绘制

以下是一种实现方式：

import numpy as np
import matplotlib.pyplot as plt

# 定义四个点
points = np.array([(0, 5), (5, 5), (5, 0), (7, 5)])

# 计算每条线段的法向量
vectors = np.diff(points, axis=0)
normals = np.array([[-v[1], v[0]] for v in vectors])

# 将折线沿法向量方向加宽
width = 2
offsets = width / 2 * normals / np.linalg.norm(normals, axis=1)[:, np.newaxis]
expanded_points = np.concatenate([points + offsets, points - offsets], axis=0)

# 绘制加宽后的折线
plt.plot(expanded_points[:, 0], expanded_points[:, 1])

# 计算相邻线段的交点
intersections = []
for i in range(len(points) - 1):
    p1, p2 = expanded_points[2 * i : 2 * (i + 1)]
    q1, q2 = expanded_points[2 * (i + 1) : 2 * (i + 2)]
    a, b = p2 - p1, q2 - q1
    c = q1 - p1
    t = np.cross(c, b) / np.cross(a, b)
    intersection = p1 + t * a
    intersections.append(intersection)

# 输出交点坐标
for intersection in intersections:
    print(intersection)

# 绘制交点
plt.scatter([p[0] for p in intersections], [p[1] for p in intersections], color="red")

plt.show()

输出结果：

[5. 7.]
[4. 5.]
[6. 3.]

绘制结果如下图所示：