krit.club logo

Shape and Space - Position and Direction

Grade 3IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Cardinal Directions: We use a compass rose to identify directions. North is at the top, South is at the bottom, East is to the right, and West is to the left. A simple way to remember the clockwise order is North, East, South, West (NEWS). Imagine a cross where North points to 1212 o'clock and East points to 33 o'clock.

•

Turns and Degrees: Movement can be described in turns. A full turn is 360∘360^{\circ}, a half turn is 180∘180^{\circ}, and a quarter turn is 90∘90^{\circ}. A 90∘90^{\circ} turn is also known as a right-angle turn, which looks like the corner of a square.

•

Clockwise and Anti-clockwise: Directions of rotation are relative to a clock face. Clockwise movement goes to the right from the top (following the path 12→3→612 \rightarrow 3 \rightarrow 6), while anti-clockwise movement goes to the left from the top (12→9→612 \rightarrow 9 \rightarrow 6).

•

Grid Coordinates: Position is often described using a grid system with a horizontal axis (xx) and a vertical axis (yy). We write coordinates as (x,y)(x, y). To find a point, we move 'along the corridor' (right) and then 'up the stairs' (up). For example, (4,2)(4, 2) means moving 44 units right and 22 units up from the origin (0,0)(0, 0).

•

Describing Movement: To describe a path, we use specific instructions combining distance and direction. For example, 'Move 33 squares North and 22 squares East.' On a visual grid, this would look like a line jumping 33 squares up and 22 squares to the right.

•

Reflections and Mirror Lines: Reflection involves 'flipping' a shape over a mirror line. Every point on the original shape is the same distance from the mirror line as the corresponding point on the reflected shape. It creates a 'mirror image' where the left and right sides appear reversed.

•

Basic Translation: Translation means sliding a shape from one position to another without turning it or changing its size. For example, translating a triangle 'right 55, down 22' means every corner of the triangle moves 55 units to the right and 22 units down on the grid.

📐Formulae

Full Turn=360∘\text{Full Turn} = 360^{\circ}

Half Turn=180∘\text{Half Turn} = 180^{\circ}

Quarter Turn (Right Angle)=90∘\text{Quarter Turn (Right Angle)} = 90^{\circ}

Coordinate Pair=(x,y)\text{Coordinate Pair} = (x, y)

💡Examples

Problem 1:

An explorer starts at the coordinate (2,3)(2, 3). He walks 44 units East and 22 units South. What is his new coordinate position?

Solution:

  1. Starting position is (x,y)=(2,3)(x, y) = (2, 3).
  2. Moving East means moving right on the grid, so we add to the xx-coordinate: 2+4=62 + 4 = 6.
  3. Moving South means moving down on the grid, so we subtract from the yy-coordinate: 3−2=13 - 2 = 1.
  4. The new coordinate is (6,1)(6, 1).

Explanation:

To solve grid movement, we translate 'East/West' into horizontal changes and 'North/South' into vertical changes.

Problem 2:

A robot is facing North. It makes a 90∘90^{\circ} turn clockwise, followed by a 180∘180^{\circ} turn anti-clockwise. Which direction is the robot facing now?

Solution:

  1. Initial direction: North.
  2. First turn: 90∘90^{\circ} clockwise from North points to East.
  3. Second turn: From East, a 180∘180^{\circ} turn (half turn) in any direction points to the opposite direction.
  4. The opposite of East is West.

Explanation:

We track the robot's facing direction step-by-step. A 180∘180^{\circ} turn always results in facing the opposite direction of the current heading.