Question

Compute the area of the triangle using coordinates. What is the area of the triangle in square units?
A (2,4)
B (9,4)
C (3,2)

14

3.5

10

7

Answer 1

To find the area of a triangle given its vertices at coordinates A(x1, y1), B(x2, y2), and C(x3, y3), we can use the formula:

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

Let's substitute the coordinates of points A, B, and C into the formula:

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

Now substituting the values into the area 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. \(3(4 - 4) = 3 \times 0 = 0\)

Putting it all together:

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

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