Question

Find the area of a triangle with vertices \( A(2, 3) \), \( B(5, 11) \), and \( C(8, 7) \).

• A. 15
• B. 18
• C. 20
• D. 25

Hint:

Remember: The area of a triangle with given vertices can be calculated using the formula that involves the coordinates of the three vertices.

Answer 1

The Correct Option is A

Step 1: Use the formula for the area of a triangle with given vertices The formula for the area of a triangle with vertices \( A(x_1, y_1) \), \( B(x_2, y_2) \), and \( C(x_3, y_3) \) is: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] For the given points: - \( A(2, 3) \), so \( x_1 = 2 \) and \( y_1 = 3 \), - \( B(5, 11) \), so \( x_2 = 5 \) and \( y_2 = 11 \), - \( C(8, 7) \), so \( x_3 = 8 \) and \( y_3 = 7 \). Step 2: Substitute the values into the formula \[ \text{Area} = \frac{1}{2} \left| 2(11 - 7) + 5(7 - 3) + 8(3 - 11) \right| \] \[ = \frac{1}{2} \left| 2 \times 4 + 5 \times 4 + 8 \times (-8) \right| \] \[ = \frac{1}{2} \left| 8 + 20 - 64 \right| \] \[ = \frac{1}{2} \left| -36 \right| \] \[ = \frac{1}{2} \times 36 = 18 \] Answer: Therefore, the area of the triangle is 18 square units. So, the correct answer is option (2).