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Position and Direction - Describing movement on a grid

Grade 4IGCSE

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

🔑Concepts

Coordinates: A pair of numbers (x, y) used to describe the exact position of a point on a grid.

The x-axis: The horizontal line at the bottom of the grid (always read this first).

The y-axis: The vertical line on the side of the grid (read this second).

The Origin: The point where the x-axis and y-axis meet, represented by the coordinates (0, 0).

Translation: Moving a shape or point from one position to another without turning it or changing its size.

Describing Movement: Movement is described in terms of 'units left/right' and 'units up/down'.

📐Formulae

Coordinate Notation: (x,y)(x, y) (Remember: 'Along the corridor and up the stairs')

Horizontal Change (Right): x+number of unitsx + \text{number of units}

Horizontal Change (Left): xnumber of unitsx - \text{number of units}

Vertical Change (Up): y+number of unitsy + \text{number of units}

Vertical Change (Down): ynumber of unitsy - \text{number of units}

💡Examples

Problem 1:

A point is located at (2, 3). If you move the point 4 units to the right and 1 unit down, what are the new coordinates?

Solution:

(6, 2)

Explanation:

Starting at x=2, moving 4 units right means adding: 2+4=62 + 4 = 6. Starting at y=3, moving 1 unit down means subtracting: 31=23 - 1 = 2. The new position is (6, 2).

Problem 2:

Describe the movement required to get from point A (1, 5) to point B (4, 5).

Solution:

3 units to the right.

Explanation:

Compare the x-coordinates: 41=34 - 1 = 3 units movement to the right. The y-coordinates are the same (5), so there is no vertical movement.

Problem 3:

A square has a vertex at (1, 1). If the square is moved '2 units left and 3 units up', where is the new vertex?

Solution:

The coordinate cannot be plotted on a standard positive-only quadrant if it goes below zero, but mathematically it is (-1, 4).

Explanation:

Subtract 2 from the x-coordinate (12=11 - 2 = -1) and add 3 to the y-coordinate (1+3=41 + 3 = 4).