Show that the points A(7 , 3) , B (6 , 1) , C ( 8 , 2) and D ( 9 , 4) taken in that order are vertices of a parallelogram . `(AS_(2))`

Prove that the points ( - 7 , - 3) , ( 5 , 10) , ( 15 , 8) and ( 3 , - 5) taken in order are the corners of a parallelogram . (AS_(2))

Show that the points A = ( 4 , 2) , B ( 7 , 5) and C ( 9 , 7) are collinear.

Show that the points (-4, -7), (-1, 2), (8, 5) and (5, -4) taken in order are the vertices of a rhombus.

Four points A(+1, -1, 1) , B(1, 3, 1), C(4, 3, 1), and D(4, -1, 1), taken in order are the vertices of

Show that the points A(-1, -2), B(4, 3), C(2, 5) and D(- 3, 0) in that order form a rectangle.

Show that the points ( - 4 , -7) , ( - 1 , 2) , ( 8 , 5) and ( 5 , -4) taken in order are the vertices of a rhombus. And find its area. (Hint : Area of rhombus =(1)/(2) xx pro-duct of its diagonals ) (AS_(2),AS_(4))

If (-2 , -1) , (a , 0) , (4 , b) and (1 , 2) are the vertices of a parallelogram then a = ....

If ( 1 , 2) , ( 4 , y) , ( x , 6) and ( 3 , 5) are the vertices of a parallelogram taken in order, find x and y . (AS_(4))

Show that the points ( 1 , 7) , ( 4 , 2) , ( - 1 , -1) and ( - 4 , 4) are vertices of a square . (AS_(2))