Question

Compute the area of the triangle using coordinates. What is the area of the triangle in square units? (2,4) (9,4) (3,2)
(1 point)
10
3.5
7
14

Answer 1

To find the area of a triangle given its vertices with coordinates \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\), 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 points \((2, 4)\), \((9, 4)\), and \((3, 2)\):

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

Now, substitute these values into the formula:

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

Calculating each term inside the absolute value:

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, substitute these results back into the equation:

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

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