Question

compute the area of the triangle using coordinates. What is the area of the triangle in square units.
Coordinates: (2,4), (9,4), (3,2)
A. 10
B. 7
C. 14
D. 3.5

Answer 1

To compute the area of a triangle given its vertices in coordinate form, we can use the formula:

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

Given the coordinates of the vertices:
- \( (x_1, y_1) = (2, 4) \)
- \( (x_2, y_2) = (9, 4) \)
- \( (x_3, y_3) = (3, 2) \)

We plug 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 substituting these values back into the area formula:

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

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