Find the centroid of `DeltaABC` whose vertices are A`(0,-1)` , B`(-2,5)` and `C (2,8)`.

Answer

To find the centroid of triangle ABC with vertices A(0, -1), B(-2, 5), and C(2, 8), we can follow these steps:

### Step 1: Identify the coordinates of the vertices
The vertices of the triangle are given as:
- A(0, -1) → (x₁, y₁)
- B(-2, 5) → (x₂, y₂)
- C(2, 8) → (x₃, y₃)

### Step 2: Write down the formula for the centroid
The formula for the centroid (G) of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃) is:
\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) \]

### Step 3: Substitute the coordinates into the formula
Now we will substitute the coordinates of points A, B, and C into the formula:
- x₁ = 0, y₁ = -1
- x₂ = -2, y₂ = 5
- x₃ = 2, y₃ = 8

Calculating the x-coordinate of the centroid:
\[ x_G = \frac{x_1 + x_2 + x_3}{3} = \frac{0 + (-2) + 2}{3} = \frac{0}{3} = 0 \]

Calculating the y-coordinate of the centroid:
\[ y_G = \frac{y_1 + y_2 + y_3}{3} = \frac{-1 + 5 + 8}{3} = \frac{12}{3} = 4 \]

### Step 4: Write the coordinates of the centroid
Thus, the coordinates of the centroid G are:
\[ G(0, 4) \]

### Final Answer
The centroid of triangle ABC is at the point (0, 4).

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