Given a point A (-1; -2), M (1; -3), K (-4; 2), P (-5; 0) find the distance between points A and M, P and K, M and K

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).

Substituting the coordinates of points A, M, P and K into this formula, we get:

| AM | = √ ((- 1 – 1) ² + (-2 – (-3)) ²) = √ ((- 2) ² + (-2 + 3) ²) = √ (2² + 1²) = √ (4 + 1) = √5.

| PK | = √ ((- 5 – (-4)) ² + (0 – 2) ²) = √ ((- 5 + 4) ² + (- 2) ²) = √ ((- 1) ² + (- 2 ) ²) = √ (1² + 2²) = √ (1 + 4) = √5.

| MK | = √ ((1 – (-4)) ² + (-3 – 2) ²) = √ ((1+ 4) ² + (-5) ²) = √ (5² + 5²) = √ (25 + 25 ) = √50 = 5√2.

Answer: | AM | = √5, | PK | = √5, | MK | = 5√2.