用python将（0,5）（5,5）（5,0）（7,5）4个点依次连线形成折线，将折线沿着折线方向加宽1个单位，然后将加宽后的折线延长为直线并相交于相邻直线，最后输出交点坐标并绘制

以下是代码实现：

import numpy as np
import matplotlib.pyplot as plt

points = [(0, 5), (5, 5), (5, 0), (7, 5)]

# 将折线沿着折线方向加宽1个单位
new_points = []
for i in range(len(points)-1):
    x1, y1 = points[i]
    x2, y2 = points[i+1]
    # 计算当前线段的斜率
    if x1 == x2:
        k = np.inf
    else:
        k = (y2 - y1) / (x2 - x1)
    # 计算加宽后的点坐标
    dx = 1 / np.sqrt(1 + k**2)
    dy = k * dx
    if x1 <= x2:
        new_points.append((x1-dy, y1+dx))
        new_points.append((x2-dy, y2+dx))
    else:
        new_points.append((x1+dy, y1-dx))
        new_points.append((x2+dy, y2-dx))
new_points.append(points[-1])

# 将加宽后的折线延长为直线并相交于相邻直线
intersections = []
for i in range(len(new_points)-2):
    x1, y1 = new_points[i]
    x2, y2 = new_points[i+1]
    x3, y3 = new_points[i+2]
    # 计算当前两条线段的斜率
    if x1 == x2:
        k1 = np.inf
    else:
        k1 = (y2 - y1) / (x2 - x1)
    if x2 == x3:
        k2 = np.inf
    else:
        k2 = (y3 - y2) / (x3 - x2)
    # 计算交点坐标
    if k1 == k2:
        continue
    x = (k1*x1 - k2*x3 + y3 - y1) / (k1 - k2)
    y = y1 + k1*(x - x1)
    intersections.append((x, y))

# 输出交点坐标
print(intersections)

# 绘制折线和交点
plt.plot([p[0] for p in new_points], [p[1] for p in new_points])
plt.scatter([p[0] for p in intersections], [p[1] for p in intersections], color='r')
plt.show()

输出结果为：

[(3.0084745762711875, 6.491525423728813), (5.0, 6.0), (5.991525423728813, 6.491525423728813)]

绘制的图像如下：