Question

What is the area of the triangle in square units
(-3,5)
(3,7)
(2,3)

Answer 1

To find the area of a triangle given its vertices, we can use the following formula based on the coordinates of the vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):

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

Given the vertices \((-3, 5)\), \((3, 7)\), and \((2, 3)\), we can assign:
- \((x_1, y_1) = (-3, 5)\)
- \((x_2, y_2) = (3, 7)\)
- \((x_3, y_3) = (2, 3)\)

Substituting these values into the area formula:

\[
\text{Area} = \frac{1}{2} \left | -3(7 - 3) + 3(3 - 5) + 2(5 - 7) \right |
\]

Calculating each term separately:

1. \( -3(7 - 3) = -3 \times 4 = -12 \)
2. \( 3(3 - 5) = 3 \times (-2) = -6 \)
3. \( 2(5 - 7) = 2 \times (-2) = -4 \)

Now substitute these values back into the equation:

\[
\text{Area} = \frac{1}{2} \left | -12 - 6 - 4 \right |
\]
\[
= \frac{1}{2} \left | -22 \right |
\]
\[
= \frac{1}{2} \times 22 = 11
\]

Thus, the area of the triangle is \( \boxed{11} \) square units.