What is the area of the triangle formed by the points O(0,0), A(4,0) and B(0,3)?

Answer

To find the area of the triangle formed by the points O(0,0), A(4,0), and B(0,3), we can use the formula for the area of a triangle given its vertices at coordinates (x1, y1), (x2, y2), and (x3, y3):

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

### Step 1: Assign the coordinates to the variables
Let:
- \( O(0,0) \) be \( (x_1, y_1) \)
- \( A(4,0) \) be \( (x_2, y_2) \)
- \( B(0,3) \) be \( (x_3, y_3) \)

So, we have:
- \( x_1 = 0, y_1 = 0 \)
- \( x_2 = 4, y_2 = 0 \)
- \( x_3 = 0, y_3 = 3 \)

### Step 2: Substitute the values into the area formula
Now substitute these values into the area formula:

\[ \text{Area} = \frac{1}{2} \left| 0(0 - 3) + 4(3 - 0) + 0(0 - 0) \right| \]

### Step 3: Simplify the expression
Calculating each term:
- The first term: \( 0(0 - 3) = 0 \)
- The second term: \( 4(3 - 0) = 12 \)
- The third term: \( 0(0 - 0) = 0 \)

Now, substituting back into the formula:

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

### Step 4: Calculate the final area
Now, calculate the area:

\[ \text{Area} = \frac{1}{2} \times 12 = 6 \]

### Conclusion
Thus, the area of the triangle formed by the points O(0,0), A(4,0), and B(0,3) is **6 square units**.

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