Final answer:
In Quadrant III of the Cartesian coordinate system, both x and y coordinates are negative. This applies to points and vectors alike, meaning for the point (x, y), x < 0 and y < 0 must be true.
Step-by-step explanation:
If the point (x, y) is in Quadrant III, then both x and y must be negative based on the definition of the Cartesian coordinate system. This is because Quadrant III is the bottom left part of the graph where both x and y coordinates are below the axes. Therefore, the conditions x < 0 and y < 0 must be true for a point to be located in Quadrant III.
In the context of vectors, the scalar components referred to as Ax and Ay also reflect this property. The vectors in the first quadrant have both scalar components positive, and vectors in the third quadrant have both scalar components negative. So, when a vector is positioned in Quadrant III, it means that its horizontal (x) component and vertical (y) component, often shown on diagrams as Ax and Ay, also have negative values. This principle is useful in understanding the orientation of vectors in a two-dimensional (x-y) graphing system.