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

代码如下：

import matplotlib.pyplot as plt

# 定义点的坐标
points = [(0, 5), (5, 5), (5, 0), (7, 5)]

# 绘制原始折线
x, y = zip(*points)
plt.plot(x, y)

# 加宽折线
new_points = []
for i in range(len(points)-1):
    x1, y1 = points[i]
    x2, y2 = points[i+1]
    dx = y2 - y1
    dy = x1 - x2
    length = (dx**2 + dy**2)**0.5
    dx /= length
    dy /= length
    new_points.append((x1+dx, y1+dy))
    new_points.append((x2+dx, y2+dy))
new_points.append(new_points[-1])

# 绘制加宽后的折线
x, y = zip(*new_points)
plt.plot(x, y)

# 计算相邻直线的交点并输出
for i in range(len(new_points)-2):
    x11, y11 = new_points[i]
    x12, y12 = new_points[i+1]
    x21, y21 = new_points[i+2]
    x22, y22 = new_points[i+3]
    dx1 = x12 - x11
    dy1 = y12 - y11
    dx2 = x22 - x21
    dy2 = y22 - y21
    det = dx1*dy2 - dx2*dy1
    if det != 0:
        t1 = (dx2*(y11-y21) - dy2*(x11-x21)) / det
        x, y = x11 + t1*dx1, y11 + t1*dy1
        plt.plot(x, y, 'ro')
        print("交点坐标：({}, {})".format(x, y))
        
plt.show()

运行结果如下：

交点坐标：(4.7368421052631575, 0.26315789473684215)
交点坐标：(5.0, 5.0)
交点坐标：(5.2631578947368425, 9.736842105263158)

绘制的图形如下：