Find the length of a segment that is part of another segment

2 segments are given. You need to determine whether the points of one segment belong to another. And what is the length of this third segment. I do it as follows:

        function Point2f(start, type, end) {
            if(type == '-') {
                return {x: start.x - end.x, y: start.y - end.y}
            }
            else if(type == '*') {
                return {x: start.x * end.x, y: start.y * end.y}
            }
            else if(type == '+') {
                return {x: start.x + end.x, y: start.y + end.y}
            }
            else if(type == '/') {
                return {x: start.x / end.x, y: start.y / end.y}
            }
        }
        
        
        function intersection(start1, end1, start2, end2) {
            var dir1 = Point2f(end1, '-', start1)
            , dir2 = Point2f(end2, '-', start2);
            
            //считаем уравнения прямых проходящих через отрезки
            var a1 = -dir1.y;
            var b1 = +dir1.x;
            var d1 = -(a1*start1.x + b1*start1.y);
            
            var a2 = -dir2.y;
            var b2 = +dir2.x;
            var d2 = -(a2*start2.x + b2*start2.y);
            
            //подставляем концы отрезков, для выяснения в каких полуплоскотях они
            var seg1_line2_start = a2*start1.x + b2*start1.y + d2;
            var seg1_line2_end = a2*end1.x + b2*end1.y + d2;
            
            var seg2_line1_start = a1*start2.x + b1*start2.y + d1;
            var seg2_line1_end = a1*end2.x + b1*end2.y + d1;
            
            // один отрезок лежит на другом отрезке
            if (seg1_line2_start * seg1_line2_end == 0 || seg2_line1_start * seg2_line1_end == 0){
                return true;
            } 
        }    

How to determine the length?