Chapter 01 • Grade 9

The Use of Coordinates

From ancient urban planning to the modern mapping of the stars. Discover the logic that structures our world.

1.1 The Origin Story

Ancient Grid Thinking

The concept of using a grid to locate objects is thousands of years old. Modern archaeology shows that ancient civilizations used rigorous coordinate-like thinking to build their worlds.

1

Sindhu-Sarasvatī Grids: Cities were built on perfect North-South and East-West "Grid Lines".

2

Baudhāyana (800 BCE): Used precise grids to construct fire altars with perfect geometry.

3

Āryabhaṭa (499 CE): Applied coordinate logic to map the motion of celestial bodies.

Fun Fact: The Ceiling Fly

Legend says René Descartes got the idea for modern coordinates while watching a fly crawl across his ceiling!

1.2 The Cartesian Plane

The Logic of Location

The coordinate plane is a 2-D space divided by two perpendicular lines called axes. Every point on this plane has a unique "address".

X-AXIS (Abscissa)

The horizontal line. Measures distance left or right from the center.

Y-AXIS (Ordinate)

The vertical line. Measures distance up or down from the center.

Origin: \( O(0, 0) \)

The point where X and Y intersect

1.3 Calculating Paths

The Distance Secret

How do we find the shortest distance between two points \( A(x_1, y_1) \) and \( D(x_2, y_2) \)? We use the Baudhāyana–Pythagoras Formula.

\( AD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Step-by-Step Example

Find distance from \( A(3, 4) \) to \( D(7, 1) \):

1

Horizontal Shift: \( 7 - 3 = 4 \)

2

Vertical Shift: \( 1 - 4 = -3 \)

3

Square & Add: \( 4^2 + (-3)^2 = 16 + 9 = 25 \)

4

Result: \( \sqrt{25} = 5 \) units

Chapter Wrap-up

Summary