Find the length of the median CD of a triangle with vertices at points A (7; 3), B (5; 1;), C (-4; 4).

Since the segment CD is the median of the triangle ABC, point D is the midpoint of the segment AB.

Let us find the abscissa x and the ordinate at point D, respectively, as the half-sum of the abscissas and the half-sum of the ordinates of points A and B:

x = (7 + 5) / 2 = 12/2 = 6;

y = (3 + 1) / 2 = 4/2 = 2.

Knowing the coordinates of the ends of the segment CD, we can calculate its length using the formula for the distance between two points on the coordinate plane:

| CD | = √ ((6 – (-4)) ^ 2 + (2 – 4) ^ 2) = √ ((6 + 4) ^ 2 + (2 – 4) ^ 2) = √ (10 ^ 2 + 2 ^ 2) = √ (100 + 4) = √104 = 2√26.

Answer: The length of the median CD is 2√26.