The centroid of `DeltaABC` is (2, 7). If the points B, C lie on x, y axes respectively and A = (4, 8) then B and C are

Answer

To find the coordinates of points B and C given the centroid of triangle ABC and the coordinates of point A, we can follow these steps:

### Step 1: Understand the Centroid Formula
The centroid (G) of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3) is given by the formula:
\[ G = \left( \frac{x1 + x2 + x3}{3}, \frac{y1 + y2 + y3}{3} \right) \]
In this case, we know the centroid G = (2, 7) and point A = (4, 8).

### Step 2: Set Up the Coordinates for B and C
Since point B lies on the x-axis, we can denote its coordinates as B(a, 0), where 'a' is the x-coordinate. Similarly, since point C lies on the y-axis, we can denote its coordinates as C(0, b), where 'b' is the y-coordinate.

### Step 3: Substitute Known Values into the Centroid Formula
Using the centroid formula, we can set up the following equations based on the coordinates:
1. For the x-coordinate:
\[ \frac{4 + a + 0}{3} = 2 \]
2. For the y-coordinate:
\[ \frac{8 + 0 + b}{3} = 7 \]

### Step 4: Solve the Equations
#### For the x-coordinate:
Multiply both sides by 3:
\[ 4 + a = 6 \]
Now, solve for 'a':
\[ a = 6 - 4 = 2 \]

#### For the y-coordinate:
Multiply both sides by 3:
\[ 8 + b = 21 \]
Now, solve for 'b':
\[ b = 21 - 8 = 13 \]

### Step 5: Write the Coordinates of B and C
Now that we have the values for 'a' and 'b', we can write the coordinates:
- B = (2, 0)
- C = (0, 13)

### Final Answer
Thus, the coordinates of points B and C are:
- B = (2, 0)
- C = (0, 13)

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