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 its vertices:

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

### Step 1: Identify the vertices
Let the points be:
- \( A(6, 0) \) → \( (x_1, y_1) \)
- \( B(2, 0) \) → \( (x_2, y_2) \)
- \( C(4, 6) \) → \( (x_3, y_3) \)

Thus, we have:
- \( x_1 = 6, y_1 = 0 \)
- \( x_2 = 2, y_2 = 0 \)
- \( x_3 = 4, y_3 = 6 \)

### Step 2: Substitute the values into the formula
Now, substituting the values into the area formula:

\[ \text{Area} = \frac{1}{2} \left| 6(0 - 6) + 2(6 - 0) + 4(0 - 0) \right| \]

### Step 3: Simplify the expression
Calculating each term:

1. \( 6(0 - 6) = 6 \times -6 = -36 \)
2. \( 2(6 - 0) = 2 \times 6 = 12 \)
3. \( 4(0 - 0) = 4 \times 0 = 0 \)

Now, substituting these back into the area expression:

\[ \text{Area} = \frac{1}{2} \left| -36 + 12 + 0 \right| = \frac{1}{2} \left| -36 + 12 \right| = \frac{1}{2} \left| -24 \right| \]

### Step 4: Calculate the absolute value and finalize the area
Taking the absolute value:

\[ \text{Area} = \frac{1}{2} \times 24 = 12 \]

Thus, the area of the triangle is \( 12 \) square units.

### Final Answer
The area of the triangle formed by the points (6, 0), (2, 0), and (4, 6) is **12 square units**.

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