[рони]

student_js29,

<script>
        sgts = [
            [{
                x: 1,
                y: 2
            }, {
                x: -3,
                y: 1
            }],
            [{
                x: -3,
                y: 5
            }, {
                x: 1,
                y: 4
            }],
            [{
                x: 4,
                y: 2
            }, {
                x: -1,
                y: 2
            }],
            [{
                x: -2,
                y: 5
            }, {
                x: 4,
                y: 1
            }]
        ];

        for (let i = 0; i < sgts.length - 1; i++) {
            let a = arrValue(sgts[i]);
            for (let j = i + 1; j < sgts.length; j++) {
                let b = arrValue(sgts[j]);
                let point = Intersection(...a, ...b);
                if (point) document.write(`отрезок ${i} пересекается с отрезком ${j} в точке x : ${point.x.toFixed(1)}, y : ${point.y.toFixed(1)}<br>`)
            }
        }

        function arrValue(arr) {
            return [arr[0].x, arr[0].y, arr[1].x, arr[1].y]
        }

        function Intersection(ax1, ay1, ax2, ay2, bx1, by1, bx2, by2) {
            let v1 = (bx2 - bx1) * (ay1 - by1) - (by2 - by1) * (ax1 - bx1),
                v2 = (bx2 - bx1) * (ay2 - by1) - (by2 - by1) * (ax2 - bx1),
                v3 = (ax2 - ax1) * (by1 - ay1) - (ay2 - ay1) * (bx1 - ax1),
                v4 = (ax2 - ax1) * (by2 - ay1) - (ay2 - ay1) * (bx2 - ax1),
                x = ((ax1 * ay2 - ax2 * ay1) * (bx2 - bx1) - (bx1 * by2 - bx2 * by1) * (ax2 - ax1)) / ((ay1 - ay2) * (bx2 - bx1) - (by1 - by2) * (ax2 - ax1)),
                y = ((by1 - by2) * x - (bx1 * by2 - bx2 * by1)) / (bx2 - bx1);
            return (v1 * v2 < 0) && (v3 * v4 < 0) && {
                x: -x,
                y: y
            };
        }
    </script>