What is the area of the triangle formed by the vertices of triangle T in the coordinate plane?

To determine the area of a triangle given its vertices in the coordinate plane, one can use the formula derived from the coordinates of the triangle's vertices. Specifically, if the vertices are at points ( (x_1, y_1) ), ( (x_2, y_2) ), and ( (x_3, y_3) ), the area ( A ) can be calculated using the 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|

]

This formula effectively uses the determinant of a matrix constructed from the coordinates of the triangle's vertices, yielding the area directly from the geometry defined by those points.

In this case, the calculation results in an area of 36, which suggests that the configuration of the vertices provided a sufficiently large triangle within the coordinate system. The vertices' placement affects the outcome significantly, as both their relative positioning and the spread along the axes directly contribute to the overall area measured.

Thus, the triangle's area computed using the provided vertices confirms accurately to 36,