Orienting Yourself: The Use of Coordinates

Vocabulary flashcards covering core terms, historical figures, and mathematical concepts from Grade 9 Mathematics Chapter 1: Orienting Yourself: The Use of Coordinates.

System of Coordinates

A structured framework (like the grid lines on a map or graph paper) that enables the use of numbers to describe the exact physical locations of points or objects.

Sindhu-Sarasvatī Civilisation

An ancient civilisation where the first systematic use of grids occurred on a massive urban scale, featuring city streets constructed in North–South and East–West directions at uniform distances of about $10\,\text{metres}$ apart.

Ujjayinī

An ancient Indian location described in early Siddhāntas (at least as early as the 4th century BCE) as marking the central longitude meridian from which all other locations were measured.

Brahmagupta

An Indian mathematician (c. 628 CE) who formalised the notion and use of zero and negative numbers as algebraic entities, making the four-quadrant Cartesian plane possible.

Al-Bīrūnī

An influential Arab scholar (c. 1000 CE) who studied the Siddhāntas, used Indian trigonometric methods to calculate city coordinates across Asia, and perfected the astrolabe.

Ömar Khayyām

A mathematician (c. 1100 CE) expert in the Indian decimal system and algebraic formalism, who became the first to solve algebraic problems using geometry by interpreting them as coordinates in the plane.

René Descartes

A French mathematician (1637 CE) who formalised the concept that any point in a two-dimensional plane can be defined by two numbers representing its distances from two perpendicular axes.

x-axis

The horizontal line in a two-dimensional coordinate system.

y-axis

The vertical line in a two-dimensional coordinate system.

Origin

The point of intersection of the x-axis and y-axis in a coordinate plane, denoted as $O$, with coordinates $(0, 0)$.

Cartesian Plane

The two-dimensional plane in which the coordinate axes are situated, also referred to as the coordinate plane or xy-plane.

Quadrants

The four regions into which the perpendicular coordinate axes divide the Cartesian plane, numbered I through IV.

x-coordinate

The perpendicular distance of a point from the y-axis, measured along the x-axis.

y-coordinate

The perpendicular distance of a point from the x-axis, measured along the y-axis.

Coordinates of a Point

An ordered pair $(x, y)$ in 2-D space where $x$ is the x-coordinate and $y$ is the y-coordinate.

Distance Formula (2-D Plane)

The formula based on the Baudhāyana–Pythagoras Theorem to calculate the distance between points $(x_1, y_1)$ and $(x_2, y_2)$, expressed as $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.