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

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 by the coordinates of its vertices:

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

Substituting the coordinates of points \( A \), \( B \), and \( C \):

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

Putting these values 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. \( 3(4 - 4) = 3 \times 0 = 0 \)

So, combining these results:

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

Thus, the area of the triangle is

\[
\boxed{7} \text{ square units.}
\]