Given: triangle ABC A (-4; 2) B (0; 5) C (-2; 4) Find the BD-median of triangle ABC.

Since BD is the median of the ABC triangle (the median divides the opposite sides into two equal parts), point D is the midpoint of the AC side.

Find the coordinates of point D: A (-4; 2), C (-2; 4).

((x1 + x2) / 2; (y1 + y2) / 2) (formula for finding the coordinates of the midpoint of the segment).

D ((- 4 – 2) / 2; (2 + 4) / 2) = D (-3; 3).

Let’s calculate the length of the median BD: B (0; 5), D (-3; 3).

d² = (x2 – x1) ^ 2 + (y2 – y1) ^ 2 (the formula for finding the length of a segment by the coordinates of the ends of the segment).

BD = √ ((- 3 – 0) ² + (3 – 5) ²) = √ ((- 3) ² + (-2) ²) = √ (9 + 4) = √13.

Answer: The length of the median BD is √13.