Compute the area of the triangle using coordinates. What is the area of the triangle in square units? (1 point) Responses 3.5 3.5 7 7 14 14 10

Answer 1

To compute the area of a triangle using coordinates, we can use the formula based on the coordinates of the vertices. If the vertices of the triangle are given by points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\), the area \(A\) of the triangle can be calculated as follows:

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

However, I need the coordinates of the triangle's vertices to perform the calculation. Please provide the coordinates of the three vertices of the triangle, so I can calculate its area.

Answer 2

The coordinates are, (2,4) (9,4) and (3,2)

Answer 3

Let's label the coordinates of the vertices of the triangle as follows:

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

Now we can apply the area formula:

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

Substituting in the coordinates:

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

Calculating each term:

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 substituting these values back into the formula:

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

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