Final answer:
The area of the triangle formed by the points (-2, 6), (-2, 0), and (7, -5) is calculated using the determinant formula for the area of a triangle, giving 30 square units. The correct answer is b.
Step-by-step explanation:
To calculate the area of the triangle formed by the points (-2, 6), (-2, 0), and (7, -5), we can use the formula for the area of a triangle with vertices at (x_1, y_1), (x_2, y_2), and (x_3, y_3):
Area = 1/2 |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|
Substituting the given points into the formula, we get:
Area = 1/2 |-2(0 - (-5)) + (-2)((-5) - 6) + 7(6 - 0)|
Area = 1/2 |10 - (-10) + 42|
Area = 1/2 |62|
Area = 31 square units
Therefore, the correct answer is b) 30 square units when rounding to the nearest even number as is standard for area calculations when the last digit is 5.