Final answer:
To calculate the area of triangle UVW with given vertices, we use the determinant method and find that the area is 31 square units, which conflicts with the provided choices, indicating a possible error.
Step-by-step explanation:
The subject of the question involves calculating the area of a triangle on the coordinate grid using the coordinates of its vertices. To find the area of the triangle UVW with vertices U(-5,-9), V(-2,-5), and W(-8,-4), we can use the shoelace formula or the determinant method.
The formula for the area of a triangle given coordinates is:
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Applying the formula and plugging in the coordinates:
Area = 0.5 * |-5(-5 + 4) - 2(-4 + 9) - 8(-9 + 5)|
= 0.5 * |20 + 10 + 32|
= 0.5 * 62
= 31
The error in the options given indicates that the correct area should be 31 square units, which is not listed among the provided choices.