Given a triangle ABC: A (1.2) B (-2.3) C (2.4). Points M, N, P are the midpoints of the sides BC

Given a triangle ABC: A (1.2) B (-2.3) C (2.4). Points M, N, P are the midpoints of the sides BC, CA and AB. Calculate the vectors MN, NP, PM.

Initially, we find the midpoints of the sides BC, AC and AB:

M = ((-2 + 2) / 2; (3 + 4) / 2) = (0; 3.5);

N = ((1 + 2) / 2; (2 + 4) / 2) = (1.5; 3);

P = ((1 – 2) / 2; (2 + 3) / 2) = (-0.5; 2.5).

Now we find the vectors MN, NP, PM:

MN = {1.5-0; 3 – 3.5} = {1.5; -0.5};

NP = {-0.5 – 1.5; 2.5 – 3} = {-2; -0.5};

PM = {0 + 0.5; 3.5 – 2.5} = {0.5; 1}.

Let’s find the modules of vectors:

| MN | = √ (1.5) ^ 2 + (-0.5) ^ 2 = √2.5;

| NP | = √ (-2) ^ 2 + (-0.5) ^ 2 = √4.25;

| PM | = √ (0.5) ^ 2 + 1 = √1.25.

Answer: √2.5; √4.25; √1.25.