Question

Compute the area of the triangle using coordinates. What is the area of the triangle in square units?
(1 point)
• 14
07
• 3.5
O 10
A(2,4
B(9,4)
C(3,2)

Answer 1

To compute the area of the triangle given the vertices A(2, 4), B(9, 4), and C(3, 2), we can use the formula for the area of a triangle based on 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 the vertices are:

- \( A(x_1, y_1) = (2, 4) \)
- \( B(x_2, y_2) = (9, 4) \)
- \( C(x_3, y_3) = (3, 2) \)

Substitute the coordinates into the formula:

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

Now calculate each term:

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

Now combine these:

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

Thus, the area of the triangle is:

\[
\text{Area} = 7 \text{ square units}
\]

However, it seems there might be a misunderstanding because this option isn't listed among the choices. Please check the coordinates or choices again if needed. Otherwise, the correct computed area, based on the provided coordinates, is **7 square units**.