Algebra - Graphs: work with coordinates in all four quadrants

The idea

A coordinate pair gives across first, then up: in (−4, 3) the −4 is the x coordinate and the 3 is the y coordinate. The two axes cut the plane into four quadrants. Top right has both coordinates positive, top left has x negative and y positive, bottom left has both negative, and bottom right has x positive and y negative. To plot a point, start at the origin (0, 0), move along the x axis, then move parallel to the y axis. Read the numbers on each axis before you start, because one square is not always one unit. Questions ask you to plot a point, name a point already marked, complete a shape such as a parallelogram, or find a midpoint. The midpoint of (−4, 3) and (2, 7) comes from averaging each coordinate, which gives (−1, 5).

What earns the marks

• Each point plotted in the right place to within half a square, even if a later part of the answer is wrong.
• A coordinate pair written in the correct order, in brackets and separated by a comma.
• Using the scale on the axes when the squares are worth more than one unit.
• A missing vertex or a midpoint that follows correctly from the points already plotted.

Common mistakes and how to put them right

• Writing the pair the wrong way round, so plotting (3, −4) when the question says (−4, 3).

• Ignoring the minus sign, so putting a point with a negative y coordinate above the x axis.

• Assuming each square is one unit when the axis is labelled in twos or fives.

• Adding the two coordinates instead of averaging them when finding a midpoint.

Exam tips

• Say "along the corridor, up the stairs" to yourself so the x coordinate always comes first.
• Check the numbers on both axes before plotting, and write the value of one square in the margin if it is not one unit.
• Mark a point with a sharp pencil cross so its position can be read accurately against the scale.