Question

In coordinate geometry, find the coordinates of the centroid of each triangle with the given vertices.

A) (0, 0)
B) (1, 1)
C) (-1, -1)
D) (2, 2)

Answer 1

The centroid of a triangle is found by averaging the x and y coordinates of its vertices. For the triangle with vertices at (0, 0), (1, 1), and (-1, -1), the centroid's coordinates are (0, 0).

Step-by-step explanation:

The centroid of a triangle is the point where the three medians of the triangle intersect. It is also known as the center of mass or the barycenter of the triangle. To find the coordinates of the centroid, one would use the formula which is simply the average of the x-coordinates and the y-coordinates of the vertices of the triangle. The coordinates of the vertices of the triangle are given as A) (0, 0), B) (1, 1), C) (-1, -1), and an additional point, D) (2, 2). To find the centroid of any triangle with these points as vertices, we can ignore the additional point D and consider only three points at a time.

Let's consider triangle ABC with vertices A (0, 0), B (1, 1), and C (-1, -1). Using the formula for the centroid (G), we get:

• The average of the x-coordinates: (0 + 1 + (-1)) / 3 = 0 / 3 = 0
• The average of the y-coordinates: (0 + 1 + (-1)) / 3 = 0 / 3 = 0

Therefore, the coordinates of the centroid (G) of triangle ABC are (0, 0).