Position and Transformation | Year 8 Mathematics (Cambridge) PDF Download

Understanding Coordinates

• Coordinates are used to locate points on a plane using pairs of numbers (x, y).
• Example: Point A is located at (2, 3) where 2 represents the x-coordinate and 3 represents the y-coordinate.

Transformations

Transformations change the position or orientation of a shape on a plane.
There are three main types:

• Translations
  • Moves a shape without rotating or flipping it.
  • Example: Translating a triangle 3 units to the right and 2 units up.
• Rotations
  • Turns a shape around a fixed point (the center of rotation).
  • Example: Rotating a square 90 degrees clockwise around the origin.
• Reflections
  • Flips a shape over a line (line of reflection).
  • Example: Reflecting a triangle over the y-axis.

Applying Transformations

• Transformations can be applied in sequences to achieve specific results.
• Example: First translate a shape, then rotate it, and finally reflect it to get a new position and orientation.

Real-World Applications

• Understanding coordinates and transformations helps in mapping, navigation, and designing graphics.
• Example: GPS systems use coordinates to pinpoint locations, and graphic designers use transformations to create animations.

Key Concepts Recap

• Coordinates help pinpoint exact positions on a plane using x and y values.
• Transformations (translations, rotations, reflections) change the position or orientation of shapes.
• Practical applications include navigation systems, graphic design, and map-making.