Number Line Convention: Location of Positive Numbers on the Cartesian Axes Evaluate the statement: “Positive numbers are represented by points to the right of the origin on the horizontal (x) axis.”

Introduction / Context:Graphical representation of quantities is fundamental to mathematics and engineering. By convention, the Cartesian x-axis increases to the right and the y-axis increases upward. This convention underlies plotting signals, Bode diagrams, IV curves, and more.

Given Data / Assumptions:

• Standard right-handed Cartesian coordinate system.
• Origin at (0, 0), horizontal axis labeled x, vertical axis labeled y.
• Uniform linear scale along axes.

Concept / Approach:

On the x-axis, positive values are located to the right of the origin, and negative values to the left. This orientation is part of the conventional right-handed system: the positive x direction to the right, positive y upwards, and when including z, the positive z comes out of the plane following the right-hand rule.

Step-by-Step Solution:

Verification / Alternative check:

Any standard math or physics text uses this orientation. Software plotting tools (MATLAB, Python, spreadsheets) default to the same layout unless explicitly redefined.

Why Other Options Are Wrong:

“False” contradicts the universal convention. “True only in polar/logarithmic” is irrelevant; the statement refers to the Cartesian x-axis. While nonstandard axes could be relabeled or reversed, the default assumption is the standard convention unless stated otherwise.

Common Pitfalls:

Confusing screen pixel coordinates (some graphics APIs have y increasing downward) with mathematical axes; always rely on the plotted axis labels and arrows when in doubt.

Final Answer:

True