Find the area of the triangle formed by the points
(1,2),(3,-4) and (-2,0)

Answer

To find the area of the triangle formed by the points (1, 2), (3, -4), and (-2, 0), 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:
- \( (x_1, y_1) = (1, 2) \)
- \( (x_2, y_2) = (3, -4) \)
- \( (x_3, y_3) = (-2, 0) \)

### Step 1: Substitute the coordinates into the formula
Substituting the coordinates into the area formula:

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

### Step 2: Simplify the expression
Now we simplify the expression inside the absolute value:

\[ = \frac{1}{2} \left| 1(-4) + 3(-2) + (-2)(2 + 4) \right| \]
\[ = \frac{1}{2} \left| -4 - 6 - 2(6) \right| \]
\[ = \frac{1}{2} \left| -4 - 6 - 12 \right| \]
\[ = \frac{1}{2} \left| -22 \right| \]

### Step 3: Calculate the area
Taking the absolute value and calculating:

\[ = \frac{1}{2} \times 22 = 11 \]

### Final Answer
Thus, the area of the triangle formed by the points (1, 2), (3, -4), and (-2, 0) is:

\[ \text{Area} = 11 \]