Given points M (1: -2), N (-2: 3) and K (3: 1), find the perimeter of the MNK.

We use the formula for the distance between two points A with coordinates (x1; y1) and B with coordinates (x2; y2)

| AB | = √ ((x1 – x2) ² + (y1 – y2) ²).

Using this formula, we find the lengths of the sides of the triangle MNK:

| MN | = √ ((1 – (-2)) ² + ((-2) – 3) ²) = √ ((1 + 2) ² + (-2 – 3) ²) = √ (3² + 5²) = √ (9 + 25) = √36;

| KN | = √ ((3 – (-2)) ² + (1 – 3) ²) = √ ((3 + 2) ² + (-2) ²) = √ (5² + 2²) = √ (25 + 4) = √29;

| MK | = √ ((1 – 3) ² + ((-2) – 1) ²) = √ ((- 2) ² + (-3) ²) = √ (2² + 3²) = √ (4 + 9) = √13.

Find the perimeter of the triangle MNK:

| MN | + | KN | + | MK | = √36 + √29 + √13.

Answer: The perimeter of triangle MNK is √36 + √29 + √13.