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Position and Direction - Coordinates in the first quadrant

Grade 4Cambridge (IGCSE)

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

🔑Concepts

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The First Quadrant is the area of a coordinate grid where both the xx (horizontal) and yy (vertical) values are positive. The grid begins at the origin (0,0)(0, 0).

A coordinate grid showing the first quadrant with x and y axes meeting at the origin (0,0).
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Coordinates are written as an ordered pair (x,y)(x, y). The first number (xx) tells you how far to move along the horizontal axis, and the second number (yy) tells you how far to move up the vertical axis. Remember: 'Along the corridor and up the stairs'.

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The x-coordinate represents the horizontal position. Moving right increases the xx value, while moving left decreases it.

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The y-coordinate represents the vertical position. Moving up increases the yy value, while moving down decreases it.

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To plot a point like (4,3)(4, 3), you start at (0,0)(0, 0), move 44 units to the right, and then 33 units up.

📐Formulae

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

Right Movement=(x+n,y)\text{Right Movement} = (x + n, y)

Left Movement=(x−n,y)\text{Left Movement} = (x - n, y)

Upward Movement=(x,y+n)\text{Upward Movement} = (x, y + n)

Downward Movement=(x,y−n)\text{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.

Problem 4:

Identify the coordinates of the vertices for the triangle plotted on the grid.

A right-angled triangle on a coordinate grid with vertices at (1,1), (4,1), and (1,4).

Solution:

A=(1,1),B=(4,1),C=(1,4)A = (1, 1), B = (4, 1), C = (1, 4),

Explanation:

Point AA is 11 unit right and 11 unit up. Point BB is 44 units right and 11 unit up. Point CC is 11 unit right and 44 units up.

Problem 5:

A rectangle has vertices at (2,2)(2, 2), (5,2)(5, 2), and (5,4)(5, 4). What are the coordinates of the fourth vertex (D)(D) to complete the rectangle?

A grid showing three points of a rectangle and the missing fourth point D at (2,4).

Solution:

D=(2,4)D = (2, 4)

Explanation:

In a rectangle, opposite sides are equal and parallel. The bottom side goes from x=2x=2 to x=5x=5 at y=2y=2. The right side goes from y=2y=2 to y=4y=4 at x=5x=5. To close the shape, we must go from x=5x=5 back to x=2x=2 at the height y=4y=4.