Final answer:
The terminal side of angle θ lies in Quadrant IV when x is positive (x>0) and y is negative (y<0). This is because positive x and negative y values are characteristic of the coordinates in that quadrant. The answer to the question is D. Quadrant IV
Step-by-step explanation:
If x>0 and y<0, then we are dealing with a scenario where the point or terminal side of the angle θ lies in a specific quadrant on a two-dimensional Cartesian coordinate system. In this system, the horizontal axis is the x-axis, and the vertical axis is the y-axis. The quadrants are numbered counterclockwise, starting from the upper right quadrant, which is Quadrant I, where both x and y are positive.
Since we are given that x (the horizontal component) is positive and y (the vertical component) is negative, we can determine that the point lies in the quadrant where the x values are positive and the y values are negative. This is Quadrant IV. Vectors in this quadrant extend to the right and downward, as they have a positive x-component and a negative y-component.
According to the coordinate system's conventions, an angle is defined as positive in the counterclockwise direction. Thus, if we consider an angle starting from the positive x-direction and sweeping towards our vector in Quadrant IV, we can affirm that the terminal side of this angle will be located in that quadrant.
The answer to the question is therefore: D. Quadrant IV, where the terminal side of the angle θ lies when x>0 and y<0.