Given points A (1: -2) B (3: 6) C (5: -2) Is the quadrilateral ABCD a parallelogram if D (7; 6)?

We have the coordinates of the four points of the quadrangle. Let’s find the lengths of its sides.

A (1; -2), B (3; 6), C (5; -2), D (7; 6).

| AB | = ((3 – 1) ^ 2 + (6 + 2) ^ 2) ^ (1/2) = (4 + 64) ^ (1/2) = 68 ^ (1/2).

| BC | = ((5 – 3) ^ 2 + (-2 – 6) ^ 2) ^ (1/2) = (4 + 64) ^ (1/2) = 68 ^ (1/2).

| CD | = ((7 – 5) ^ 2 + (6 + 2) ^ 2) ^ (1/2) = (4 + 64) ^ (1/2) = 68 ^ (1/2).

| AD | = ((7 – 1) ^ 2 + (6 +2) ^ 2) ^ (1/2) = (36 + 64) ^ (1/2) = 10.

| AB | = | BC | = | CD |.

| AD | = / = | BC |.

The lengths of the opposite sides of the quadrilateral are not equal, which means that it is not a parallelogram.