Tutorial on Use of points, lines, polygons and curved lines.

🔷 1. Points

📌 Definition:

A point is a location in space. It has no length, width, or depth—just a position.

✏️ Notation:

• Typically represented by a dot and a letter, e.g., Point A or A(x,y)A(x, y)A(x,y).

💡 Use of Points:

• Define positions on a plane or space.
• Serve as endpoints or intersections.
• Used as reference markers in design and mapping.

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🔷 2. Lines

📌 Definition:

A line is a straight, one-dimensional figure that extends infinitely in both directions. A line segment has two endpoints.

✏️ Notation:

• Line through A and B: AB↔\overleftrightarrow{AB}AB
• Line segment: AB‾\overline{AB}AB

💡 Use of Lines:

• Connect points.
• Represent paths, edges, or borders.
• Form the sides of polygons.
• Used in diagrams, technical drawings, and geometry proofs.

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🔷 3. Polygons

📌 Definition:

A polygon is a closed shape formed by a series of connected straight lines (segments) called sides.

✏️ Examples:

• Triangle: 3 sides
• Quadrilateral: 4 sides
• Pentagon: 5 sides
• Hexagon: 6 sides, etc.

💡 Use of Polygons:

• Represent surfaces or areas (maps, floor plans).
• Create complex shapes in graphic design and CAD.
• Analyze area, perimeter, and other geometric properties.
• Used in mesh modeling (3D design) and game development.

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🔷 4. Curved Lines

📌 Definition:

A curved line continuously changes direction without forming sharp angles. It can be open or closed (like circles or ellipses).

✏️ Types:

• Arcs (part of a circle)
• Freeform curves (Bezier curves, splines)
• Closed curves (circles, ellipses)

💡 Use of Curved Lines:

• Create natural or organic shapes.
• Add aesthetics and fluidity in design.
• Represent topographical features (in GIS).
• Model smooth motions or transitions in animations.

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🧠 Summary Table:

Concept	Representation	Use
Point	Dot, coordinates	Positioning, marking locations
Line	Straight path	Connecting points, defining directions
Polygon	Closed shape	Representing surfaces/areas, creating solid shapes
Curved Line	Smooth path	Organic design, motion paths, complex shapes

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✍️ Practical Applications

Field	Usage Example
Art/Design	Vector illustrations (Adobe Illustrator, Figma)
Geometry	Solving theorems, constructions
GIS/Mapping	Points (locations), lines (roads), polygons (zones, buildings)
Programming	Drawing with canvas/SVG (HTML5, Python turtle, Processing)
Engineering/CAD	Design parts, schematics using lines, curves, and polygons