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Geometry - Position, direction, and movement

Grade 3IGCSE

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

🔑Concepts

Coordinate Grids: Locating positions on a grid using coordinates (x, y).

Reading Coordinates: Always read the horizontal (x-axis) value first, then the vertical (y-axis) value ('Along the corridor, then up the stairs').

Compass Directions: Identifying the four main cardinal points: North (N), South (S), East (E), and West (W).

Movement and Translation: Moving a shape or point a specific number of units left, right, up, or down without turning it.

Turns and Rotation: Describing turns as clockwise or anti-clockwise, and using terms like quarter turn (right angle), half turn, and full turn.

📐Formulae

Position = (x, y)

1 quarter turn=90 (right angle)1 \text{ quarter turn} = 90^\circ \text{ (right angle)}

1 half turn=180 (2 right angles)1 \text{ half turn} = 180^\circ \text{ (2 right angles)}

1 full turn=360 (4 right angles)1 \text{ full turn} = 360^\circ \text{ (4 right angles)}

💡Examples

Problem 1:

A treasure map has a grid. A gold coin is located at 3 units to the right and 5 units up from the starting point (0,0). What are the coordinates of the gold coin?

Solution:

(3,5)(3, 5)

Explanation:

To find coordinates, we list the horizontal distance (x) first and the vertical distance (y) second. Since we move 3 units right and 5 units up, the coordinate is (3, 5).

Problem 2:

Robot 'Z' is facing North. It makes a quarter turn clockwise. Which direction is it facing now?

Solution:

East

Explanation:

A clockwise turn follows the direction of a clock's hands. Starting at North, a 9090^\circ (quarter) turn to the right leads to East.

Problem 3:

Point A is at (2,2)(2, 2). If you move Point A 3 squares to the right and 1 square down, what are its new coordinates?

Solution:

(5,1)(5, 1)

Explanation:

Moving right increases the x-coordinate: 2+3=52 + 3 = 5. Moving down decreases the y-coordinate: 21=12 - 1 = 1. The new position is (5,1)(5, 1).