# Definition:Homogeneous Cartesian Coordinates

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*This page is about Homogeneous Cartesian Coordinates. For other uses, see Homogeneous.*

## Definition

Let $\CC$ denote the Cartesian plane.

Let $P = \tuple {x, y}$ be an arbitrary point in $\CC$.

Let $x$ and $y$ be expressed in the forms:

\(\ds x\) | \(=\) | \(\ds \dfrac X Z\) | ||||||||||||

\(\ds y\) | \(=\) | \(\ds \dfrac Y Z\) |

where $Z$ is an arbitrary real number.

$P$ is then determined by the ordered triple $\tuple {X, Y, Z}$, the terms of which are called its **homogeneous Cartesian coordinates**.

## Also denoted as

This can also be presented as:

- $P = \tuple {X : Y : Z}$

## Also see

- Results about
**homogeneous Cartesian coordinates**can be found**here**.

## Sources

- 1933: D.M.Y. Sommerville:
*Analytical Conics*(3rd ed.) ... (previous) ... (next): Chapter $\text {II}$. The Straight Line: $9$. Parallel lines. Points at infinity