Question

use the formulas to find the centroid of the triangle with vertices (0, 0), (a, 0), and (a, b), where a > 0 and b > 0.

Answer 1

To find the centroid of the triangle, average the x-coordinates and the y-coordinates of the vertices.

Step-by-step explanation:

To find the centroid of a triangle with vertices (0, 0), (a, 0), and (a, b), where a > 0 and b > 0, we can use the formulas for the centroid. The centroid is the average of the x-coordinates and the average of the y-coordinates of the vertices.

The x-coordinate of the centroid is given by (0 + a + a) / 3 = 2a/3.

The y-coordinate of the centroid is given by (0 + 0 + b) / 3 = b/3.

Therefore, the coordinates of the centroid are (2a/3, b/3).

Answer 2

To find the centroid of a triangle with given vertices, we can use the formulas (x₁ + x₂ + x₃)/3 and (y₁ + y₂ + y₃)/3. Substituting the vertex coordinates into the formulas gives us the coordinates of the centroid.

Step-by-step explanation:

The centroid of a triangle is the point where the medians of the triangle intersect. To find the centroid, we can use the formulas:

x-coordinate of centroid = (x₁ + x₂ + x₃)/3

y-coordinate of centroid = (y₁ + y₂ + y₃)/3

Given that the vertices of the triangle are (0, 0), (a, 0), and (a, b), we can substitute these values into the formulas to find the centroid coordinates.

x-coordinate of centroid = (0 + a + a)/3 = (2a)/3

y-coordinate of centroid = (0 + 0 + b)/3 = b/3

Therefore, the coordinates of the centroid are (2a/3, b/3).