# Find the center of gravity of the triangle ABC, if a (-4; 10), in (2; 8), with (-4; -6).

July 25, 2021 | education

| 1. The center of gravity of the triangle is at the intersection of the medians.

2. Find the coordinates of the point M – the midpoint of the side BC:

A (-4; 10);

B (2; 8);

C (-4; -6).

x (M) = (2 – 4) / 2 = -2/2 = -1;

y (M) = (8 – 6) / 2 = 2/2 = 1;

M (-1; 1).

3. The point O of the intersection of the medians divides them in a ratio of 2: 1:

AO: MO = 2: 1.

Therefore, the coordinates of point O can be determined by the formula:

x (O) = x (M) + (x (A) – x (M)) / 3;

y (O) = y (M) + (y (A) – y (M)) / 3;

x (O) = -1 + (-4 + 1) / 3 = -1 + (-3) / 3 = -1 – 1 = -2;

y (O) = 1 + (10 – 1) / 3 = 1 + 9/3 = 1 + 3 = 4;

O (-2; 4).

Answer: (-2; 4).

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