Definition:Cartesian Coordinate System/Y Coordinate

Definition

Consider a Cartesian coordinate system $C$ with a $y$-axis.

Let a point $Q$ be positioned in $C$.

Let $y$ be the length of the line segment from the origin $O$ to the foot of the perpendicular from $Q$ to the $y$-axis.

Then $y$ is known as the $y$ coordinate.

If $Q$ is in the positive direction along the real number line that is the $y$-axis, then $y$ is positive.

If $Q$ is in the negative direction along the real number line that is the $y$-axis, then $y$ is negative.

Also known as

An archaic term for the $y$ coordinate which is sometimes seen is ordinate.

Some sources hyphenate: $y$-coordinate.

Also see

• Definition:X Coordinate
• Definition:Z Coordinate

• Results about $y$ coordinates can be found here.

Sources

• 1934: D.M.Y. Sommerville: Analytical Geometry of Three Dimensions ... (previous) ... (next): Chapter $\text I$: Cartesian Coordinate-system: $1.1$. Cartesian coordinates
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Cartesian coordinate system
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): $y$-coordinate
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Cartesian coordinate system
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): $y$-coordinate