The area of triangle formed by the points (6,0),(2,0) and (4,6)is______.

Options

A. 18 sq. units
B. 10 sq. units
C. 24 sq. units
D. 12 sq. units

Answer

To find the area of the triangle formed by the points (6,0), (2,0), and (4,6), we can use the formula for the area of a triangle given by the coordinates of its vertices. The formula is:

\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the vertices of the triangle.

### Step-by-Step Solution:

1. **Identify the coordinates of the points**:
- Let \( (x_1, y_1) = (6, 0) \)
- Let \( (x_2, y_2) = (2, 0) \)
- Let \( (x_3, y_3) = (4, 6) \)

2. **Substitute the coordinates into the area formula**:
\[ \text{Area} = \frac{1}{2} \left| 6(0 - 6) + 2(6 - 0) + 4(0 - 0) \right| \]

3. **Calculate each term**:
- First term: \( 6(0 - 6) = 6 \times -6 = -36 \)
- Second term: \( 2(6 - 0) = 2 \times 6 = 12 \)
- Third term: \( 4(0 - 0) = 4 \times 0 = 0 \)

4. **Combine the terms**:
\[ \text{Area} = \frac{1}{2} \left| -36 + 12 + 0 \right| = \frac{1}{2} \left| -24 \right| \]

5. **Calculate the absolute value**:
\[ \text{Area} = \frac{1}{2} \times 24 = 12 \]

6. **Final Result**:
The area of the triangle is \( 12 \) square units.