IGCSE Maths / Graphs of straight lines
Coordinates in all four quadrants revision notes
Edexcel International GCSE Maths (4MA1), chapter 6: Graphs of straight lines, specification point 3.3c-f. Free lesson.
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Coordinates are written as (x, y): x gives the horizontal position and y gives the vertical position. Knowing the order and the signs lets you plot or identify points in all four quadrants and on the axes.
Read coordinates in the right order
A coordinate pair is written (x, y). The first number tells you how far to move horizontally from the origin, where the axes cross. The second tells you how far to move vertically. Think “along the corridor, then up the stairs”: x first, then y. A positive x value means move right; a negative x value means move left. A positive y value means move up; a negative y value means move down. The origin is (0, 0), where the two axes meet.
Plot points in all four quadrants
The quadrants are the four regions around the axes. The signs of x and y show which direction to move, and therefore which quadrant contains the point. (+, +) is top right. (−, +) is top left. (−, −) is bottom left. (+, −) is bottom right.
Keep x and y in the right places
Swapping the numbers changes the point because the first number is always the horizontal distance. For example, (2, 5) means 2 right and 5 up. Moving 5 right and 2 up would plot (5, 2), a different point. Write and read coordinates as (x, y), never (y, x). The two positions only give the same point when the coordinates are equal.
Find points on the axes
A point on an axis has no movement in the direction perpendicular to that axis. This makes one coordinate zero. On the x axis, there is no vertical movement, so y = 0. For example, (4, 0). On the y axis, there is no horizontal movement, so x = 0. For example, (0, 4). A point 6 units left of the origin on the x axis is (−6, 0).