The points A(-a,-b) , B (0,0), C(a, b) and D (a², a b ) are

Step-by-step solution

(D) Distance between the points A(-a,-b) and B(0,0)= (0+a)²+(0+b)² = a²+b² Distance between the points B(0,0) and C(a, b), (a-0)²+(b-0)² = a²+b² Distance between the points C(a, b) and D (a², a b ) array l = (a²-a )²+(a b-b)² = [a(a-1)]²+[b(a-1)]² = a²(a-1)²+b²(a-1)² = (a²+b² )(a-1)² =(a-1) a²+b² array Similarly, distance between the points A(-a,-b) and D (a², a b ) aligned = (a²+a )+(a b+b)² &=(a+1) a²+b² A B+B C+C D &= a²+b² + a²+b² +(a-1) a²+b² &=(a+1) a²+b² =A D aligned Hence the point are collinear.