Question

Как через точку квадратной поляны провести тропинку так, чтобы она отсекла участок наименьшей площади？

Answer 1

Дальше постарайтесь сделать сами. Если что, я подкорректирую.
Общий вид ЛЮБОЙ прямой:
y=mx+b
Подставляем в неё точку M:
1=4m+b => b=1-4m
Подставляем:
y=mx-4m+1. Это и есть общее уравнение прямой проходящей через точку M, отсекающую треугольник в I квадранте.

Answer 2

Drawing a Path through a Square Field to Enclose the Smallest Area

To draw a path through a square field that encloses the smallest area, you can create a path that divides the square into two equal areas. This can be achieved by drawing a diagonal line from one corner of the square to the opposite corner. This diagonal line will divide the square into two right-angled triangles, each with half the area of the square. By doing so, you effectively enclose the smallest area within the path.

Key Points: - Drawing a diagonal line from one corner of the square to the opposite corner will divide the square into two equal areas, enclosing the smallest area within the path.

The most efficient way to divide a square into two equal areas is by drawing a diagonal line from one corner to the opposite corner.

This method ensures that the enclosed area is minimized, as the diagonal line divides the square into two right-angled triangles, each with half the area of the square.

Conclusion

Drawing a diagonal line through a square field is the most effective way to create a path that encloses the smallest area within the square.