Final answer:
The positive vertical axis refers to positive values on the y-axis, while the negative horizontal axis refers to negative values on the x-axis. Being at the origin means a point is at the (0, 0) coordinate. Quadrant III contains points with both negative x and y values.
Step-by-step explanation:
When discussing coordinate systems in mathematics, particularly the Cartesian coordinate system, various terms are used to describe locations in relation to the axes and quadrants defined by the system.
A) Explanation of the positive vertical axis
The positive vertical axis refers to the y-axis, where moving upwards from the origin represents increasing positive values. In a two-dimensional coordinate system, points located on the positive vertical axis have a zero x-coordinate and a positive y-coordinate.
B) Explanation of the negative horizontal axis
The negative horizontal axis refers to the portion of the x-axis that extends to the left of the origin. Points on this axis have a negative x-coordinate and a zero y-coordinate.
C) Explanation of being at the origin
Being at the origin means that an object or point is located at the zero point of both the x-axis and the y-axis, which is the point where these two axes intersect.
D) Explanation of being in Quadrant III
Quadrant III is the region of the Cartesian plane where both x and y coordinates are negative. Points in this quadrant have negative x-values and negative y-values.