Question

Given the 3 points A(0;1) , B(5;0) , and C(4;2)

a) Find the coordinates of M the midpoint of [AB]

b) Find the coordinates of G the center of gravity of the triangle ABC .​

Answer 1

The answer is below

Explanation:

a) If O(x, y) is the midpoint between two points X(x₁, y₁) and Y(x₂, y₂)m then the coordinates of O is:

x = (x₁ + x₂)/2; y = (y₁ + y₂) / 2

Since M(x, y) is the midpoint of AB, then the coordinates of M is:

x = (0 + 5) / 2 = 2.5; y = (1 + 0)/2 = 0.5

M = (2.5, 0.5)

b) The center of gravity is gotten by finding the average of the x coordinates and the y coordinates of the vertices of the triangle.

Let O(x, y) be the center of gravity of triangle ABC, hence;

x = (0 + 5 + 4) / 3 = 3

y = (1 + 0 + 2) / 3 = 1

O = (3, 1)