Question

Compute the area of the triangle using coordinates. What is the area of the triangle in square units?

(1 point)

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*

3.5

7

14

10

A: (2,4)
B: (9,4)
C (3,2)

Answer 1

To find the area of the triangle formed by the points A(2, 4), B(9, 4), and C(3, 2) using their coordinates, we can use the formula for the area of a triangle given by its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):

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

Substituting the coordinates of the points:

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

We plug these values into the formula:

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

Calculating each term:

\[
= \frac{1}{2} \left| 2 \cdot 2 + 9 \cdot (-2) + 3 \cdot 0 \right|
\]
\[
= \frac{1}{2} \left| 4 - 18 + 0 \right|
\]
\[
= \frac{1}{2} \left| -14 \right|
\]
\[
= \frac{1}{2} \cdot 14 = 7
\]

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

The answer is \(7\).