In the triangle ABC A (3; 5) B (-11; 1) C (1; -3). Find the length of the median AM

Let the coordinates of the vertices of the triangle ABC be equal: A (3; 5); B (-11; 1); C (1; -3). Let us determine the coordinates of the currents M, knowing that VM = MS (middle of the BC side).

xM = (xB + xC) / 2 = (-11 + 1) / 2 = -10/2 = -5;

yM = (yB + US) / 2 = (1 – 3) / 2 = -2/2 = -1; M (-5; -1)

We apply the coordinates of the point A (xA; yA) = A (3; 5).

The length of AM is determined by the formula: AM = √ [(xA – xM) ^ 2 + (xA – xM) ^ 2] = √ [(5 + 3) ^ 2 + (5 + 1) ^ 2] = √ (8 ^ 2 + 6 ^ 2) = √ (64 + 36) = √100 = 10 (cm).

Answer: the length of the median is AM = 10.