Find the perimeter of triangle MPK if М (2; -5) P (-5; -2) K (2; 5).

Let’s use the formula for the distance between two points A and B on the coordinate plane with coordinates A (x1; y1) and B (x2; y2):

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

We find the length of the MP side:

| MР | = √ ((2 – (-5)) ² + (-5 – (-2)) ²) = √ ((2 + 5) ² + (-5 + 2) ²) = √ (7² + 3²) = √ (49 + 9) = √58;

We find the length of the side of the MK:

| MK | = √ ((2 – 2) ² + (-5 – 5) ²) = √ (0² + (-10) ²) = √ (100 = 10.

We find the length of the side of the РK:

| РK | = √ ((- 5 – 2) ² + (-2 – 5) ²) = √ ((- 7) ² + (-7) ²) = √ (49 + 49) = 2√7.

Find the perimeter of this triangle:

| MР | + | MK | + | РK | = √58 + 10 + 2√7.

Answer: The perimeter of this triangle is √58 + 10 + 2√7.