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Position and Direction - Coordinates in the first quadrant

Grade 4IGCSE

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

🔑Concepts

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The Coordinate Grid: A 2D surface formed by two perpendicular lines: the horizontal x-axis and the vertical y-axis.

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

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Ordered Pairs: Coordinates are written as (x, y), where 'x' is the horizontal distance and 'y' is the vertical distance.

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Reading Coordinates: Always read the horizontal value (along the corridor) before the vertical value (up the stairs).

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First Quadrant: The area of the grid where both x and y values are positive.

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Translation: Moving a point or a shape to a different position by sliding it up, down, left, or right.

📐Formulae

extCoordinatePair=(x,y) ext{Coordinate Pair} = (x, y)

extRightMovement=(x+n,y) ext{Right Movement} = (x + n, y)

extLeftMovement=(x−n,y) ext{Left Movement} = (x - n, y)

extUpwardMovement=(x,y+n) ext{Upward Movement} = (x, y + n)

extDownwardMovement=(x,y−n) ext{Downward Movement} = (x, y - n)

💡Examples

Problem 1:

A point is located 5 units to the right of the origin and 3 units up. Write its coordinates.

Solution:

(5, 3)

Explanation:

The first number (x) represents the horizontal distance from the origin (5), and the second number (y) represents the vertical distance (3).

Problem 2:

Start at point (2, 4). Move 3 units to the right and 1 unit down. What are the new coordinates?

Solution:

(5, 3)

Explanation:

Moving right increases the x-value: 2+3=52 + 3 = 5. Moving down decreases the y-value: 4−1=34 - 1 = 3.

Problem 3:

Points are plotted at (1, 1), (1, 5), and (5, 5). If these are three corners of a square, what is the coordinate of the fourth corner?

Solution:

(5, 1)

Explanation:

To complete the square, the fourth point must be on the same horizontal level as (1, 1), meaning y=1y=1, and the same vertical line as (5, 5), meaning x=5x=5.