Short answers, pulled from the story.
2D computer graphics began in the early 1950s when computer scientists chose to remain flat rather than simulate three-dimensional realism. This field was born from the necessity of vector graphics devices that could draw lines and shapes with mathematical precision.
2D computer graphics relies on Euclidean geometry and linear algebra to define images. Engineers utilize homogeneous coordinates to transform non-linear translations into linear matrix operations that allow for rotation and scaling.
Vector graphics relied on geometric models and mathematical equations to define lines and curves while offering infinite scalability. Raster graphics emerged as a cheaper alternative using pixel grids composed of rectangular arrays of colored dots.
Dedicated graphics processing units and co-processors known as blitters enabled the rapid manipulation of pixel data. Chips such as the NEC μPD7220 and the Sega VDP handled the heavy lifting of drawing sprites and backgrounds.
The democratization of 2D computer graphics began in 1984 with the release of MacPaint. This software introduced direct manipulation to the masses and was followed by tools like MacDraw and Adobe Photoshop.