A (-2, 2), B (8, 2) and C (4, -4) are the vertices of a parallelogram ABCD. By plotting the given points on a graph paper; find the co-ordinates of the fourth vertex D.

Also, from the same graph, state the co-ordinates of the mid-points of the sides AB and CD.

Plot the points A (-2, 2), B (8, 2) and C (4, -4) on the graph paper. Join point A with B and B with C.

From the graph, it is clear that the horizontal distance between the points A (-2, 2) and B (8, 2) is 10 units and the vertical distance between the points B (8, 2) and C (4, -4) is 6 units. Therefore, the vertical distance between the points A (-2, 2) and D must be 6 units and the horizontal distance between the points C (4, -4) and D must be 10 units.

Now, complete the parallelogram ABCD and read the coordinates of point D. As shown on the graph, D = (-6, -4).

The midpoint of AB lies exactly halfway between A(-2, 2) and B(8, 2). On the graph, this midpoint is at (3, 2), as it is 5 units from both A and B.

The midpoint of CD lies exactly halfway between C (4, -4) and B (-6, -4). On the graph, this midpoint is at (-1, -4), as it is 5 units from both C and D.

Hence, D = (-6, -4) and mid point of AB = (3, 2) and CD = (-1, -4).