Question

The area of the triangle whose vertices are A(2, 3), B(−1, 0) and C(2, −4) (in square units) is

• A. 11.5
• B. 10
• C. 10.5
• D. 11

Hint:

When calculating the area of a triangle using its vertices, use the formula involving the determinant of the matrix formed by the coordinates.

Answer 1

The Correct Option is C

Step 1: Formula for the Area of a Triangle.
The formula for the area of a triangle given its vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \) is: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

Step 2: Apply the given coordinates.
For \( A(2, 3) \), \( B(-1, 0) \), and \( C(2, -4) \), we substitute the coordinates into the formula: \[ \text{Area} = \frac{1}{2} \left| 2(0 - (-4)) + (-1)((-4) - 3) + 2(3 - 0) \right| \] \[ \text{Area} = \frac{1}{2} \left| 2(D) + (-1)(-7) + 2(C) \right| \] \[ \text{Area} = \frac{1}{2} \left| 8 + 7 + 6 \right| = \frac{1}{2} \times 21 = 10.5 \]

Step 3: Conclusion.
Therefore, the area of the triangle is \( 10.5 \) square units.

Final Answer: 10.5.