Position, Direction and Movement Chapter Notes | Year 4 Mathematics IGCSE (Cambridge) - Class 4 PDF Download

Position and movement

• The objective is to use eight compass directions to describe direction.
• Use coordinates to describe position.
• Understanding position and movement is essential for navigation (e.g., at sea or in unfamiliar places) and for reading maps to plan routes.
• Compass directions:
  • Eight directions: North (N), North-East (NE), East (E), South-East (SE), South (S), South-West (SW), West (W), North-West (NW).
  • Used to describe movement, e.g., traveling north-west from a starting point to reach a specific town on a map.
  • Example: A route from Ibri to Sheki might involve movements like 1 square north-west, 1 square north-east, 1 square north-west, 1 square north-east.
• Coordinates:
  • Describe a point’s position on a grid using an ordered pair (x, y).
  • x: Horizontal distance along the x-axis (left to right).
  • y: Vertical distance along the y-axis (bottom to top).
  • Example: To mark (3, 5), locate x = 3 on the x-axis, then move up to y = 5 on the y-axis, marking the intersection with an X.
  • Common mistake: Swapping x and y values, e.g., interpreting (4, 1) as (1, 4).
• Quadrant:
  • The coordinate grid’s first quadrant (used here) includes positive x and y values, ranging from 0 to a specified maximum (e.g., 6).
• Applications include designing patterns, reading maps, and planning travel routes, such as navigating roads around Cambridge.

Reflecting 2D shapes

• The objective is to sketch the reflection of a 2D shape on a grid.
• Reflections create mirror images of shapes over a mirror line, useful for designing patterns and displays.
• Reflection process:
  • A mirror line (vertical or horizontal) acts as the axis of reflection.
  • Each vertex of the shape is reflected to a point equidistant from the mirror line on the opposite side.
  • Example: For a shape with vertices A, B, C on a grid:
    • If vertex A is 2 squares from a vertical mirror line, its reflection is 2 squares on the opposite side.
    • If vertex B is 2 squares from the mirror line, its reflection is 2 squares on the opposite side.
    • If vertex C is 3 squares from the mirror line, its reflection is 3 squares on the opposite side.
  • Join the reflected vertices to form the mirrored shape.
• Properties of reflections:
  • The reflected shape is congruent to the original, with the same area and shape but mirrored orientation.
  • When a shape is reflected over a mirror line along one of its edges, the original and reflected shapes combine to form a new shape, e.g., a parallelogram and its reflection may form a hexagon.
  • Lines drawn between each original vertex and its reflected vertex are perpendicular to the mirror line and bisected by it.
• Reflections with coordinates:
  • For a shape with vertices at coordinates, e.g., (0, 2), (0, 5), (1, 2), (1, 5), reflecting over a mirror line changes the coordinates predictably based on the mirror line’s position.
  • Example: Reflecting over a vertical mirror line at x = 2 would adjust the x-coordinates while keeping y-coordinates constant, depending on the distance from the mirror line.
• Using a grid improves accuracy by allowing precise measurement of distances from the mirror line.