Question

What is the area of the triangle in this coordinate plane?
Responses

17.5 units²
17.5 units²

21.0 units²
21.0 units²

35.5 units²
35.5 units²

49.0 units²
49.0 units²
A graph with a triangle drawn on it. One point of the triangle touches the y axis

Answer 1

To find the area of a triangle on a coordinate plane, you can use the formula:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

If you have coordinates for the vertices of the triangle, you can also use the determinant formula for the area:

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

Where \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are the coordinates of the three vertices of the triangle.

Since you have not provided specific coordinates for the triangle's vertices, I can't calculate the exact area. Based on the options you've given (17.5 units², 21.0 units², 35.5 units², and 49.0 units²), you may need to apply one of these formulas using the vertices' coordinates to find the correct area.

If you can provide the coordinates of the triangle, I can help you determine the area.