Position and Transformation | Year 9 Mathematics (Cambridge) PDF Download

Coordinates and Transformations

• Coordinates in a Plane:
  • Coordinates describe the position of a point on a plane using two numbers: (x, y).
  • Example: Point A is at (3, 5).
• Translations (Slides):
  • Moving a shape without rotating or flipping it.
  • Example: Slide triangle ABC 3 units to the right and 2 units up.

Reflections, Rotations, and Translations

• Reflections:
  • Flipping a shape over a line called the line of reflection.
  • Example: Reflect shape XYZ over the y-axis.
• Rotations:
  • Turning a shape around a point called the center of rotation.
  • Example: Rotate square WXY 90 degrees clockwise around point W.
• Translations:
  • Sliding a shape without changing its size or shape.
  • Example: Translate rectangle PQR 4 units left and 5 units down.

Symmetry

• Lines of Symmetry:
  • A line that divides a shape into two mirrored halves.
  • Example: Triangle DEF has 1 line of symmetry.
• Rotational Symmetry:
  • A shape that looks the same after a rotation of less than a full turn.
  • Example: A regular hexagon has 6-fold rotational symmetry.

Examples

• Coordinates Example: Describe the coordinates of points A, B, and C: A(2, 4), B(0, -1), C(-3, 2).
• Reflection Example: Reflect triangle LMN over the x-axis. What are the new coordinates?
• Rotation Example: Rotate square PQRS 180 degrees around point P. Determine the new positions of points Q, R, and S.
• Translation Example: Translate rectangle UVWX 5 units to the right and 3 units down. What are the new coordinates of vertex U?
• Symmetry Example: Identify the lines of symmetry for shape ABCDEFG.

Summary

Position and transformation involve understanding how shapes move and reflect on a coordinate plane. By mastering these concepts, you can accurately describe and manipulate shapes in different positions and orientations.