Compute the area of the triangle using coordinates. What is the area of the triangle in square units? (1 point) Responses 14 14 3.5 3.5 7 7 10

Question

The triangle's coordinates are, A: (2, 4) B: )9, 4) and C: (3, 2)

Answer 1

To compute the area of the triangle formed by the points \( A(2, 4) \), \( B(9, 4) \), and \( C(3, 2) \), we can use the formula for the area of a triangle given its vertices:

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

Where:

• \( (x_1, y_1) = (2, 4) \)
• \( (x_2, y_2) = (9, 4) \)
• \( (x_3, y_3) = (3, 2) \)

Substituting the coordinates into the formula:

\[ \text{Area} = \frac{1}{2} \left| 2(4 - 2) + 9(2 - 4) + 3(4 - 4) \right| \]

Calculating each term:

1. \( 2(4 - 2) = 2 \times 2 = 4 \)
2. \( 9(2 - 4) = 9 \times (-2) = -18 \)
3. \( 3(4 - 4) = 3 \times 0 = 0 \)

Now plug in these values:

\[ \text{Area} = \frac{1}{2} \left| 4 - 18 + 0 \right| = \frac{1}{2} \left| -14 \right| = \frac{1}{2} \times 14 = 7 \]

Thus, the area of the triangle is \( \boxed{7} \) square units.