Final answer:
The triangular region with vertices (0, 0), (9, 1), and (1, 9) is located in Quadrant I, since all vertices have positive x and y coordinates. The correct answer to the question is: a) Quadrant I.
Step-by-step explanation:
The question asks where the triangular region defined by three vertices (0, 0), (9, 1), and (1, 9) is located in a Cartesian coordinate system. Considering these points, they all have positive x and y coordinates, which means that they fall into the first quadrant of the Cartesian plane. Consequently, the triangular region they define is also located in Quadrant I.
To explain this step-by-step, first, we look at the vertex (0, 0), which is the origin and it belongs to no specific quadrant but is the reference point for all other quadrants. Next, the point (9, 1) has a positive x-coordinate and a positive y-coordinate, which places it in Quadrant I. Similarly, the point (1, 9) has both coordinates positive, so it too is in Quadrant I. Since all three vertices are in Quadrant I, the triangle they form is fully contained within this quadrant.