Coordinates.
Locate a point with an ordered pair and read position across all four quadrants.
Use Cartesian coordinates · read axes and scales · identify positions in two dimensions
Across first, then up or down
A coordinate grid is an address system for points. Two perpendicular number lines meet at the origin, where both readings are zero. The horizontal line is the x-axis and the vertical line is the y-axis.
To locate (3, 2), start at the origin, move 3 units horizontally and then 2 units vertically. The order is always horizontal first, vertical second. A negative reading reverses the direction on its own axis, not on both axes.
Cartesian coordinates locate a point using an ordered pair (x, y). Start at the origin (0, 0), move along the horizontal x-direction, then in the vertical y-direction.
P is in quadrant I. The x-coordinate comes first.
Positive and negative directions
Positive x is right; negative x is left. Positive y is up; negative y is down.
A = (−4, 2) is 4 units left and 2 units up.
Points on the axes
On the x-axis, y = 0: for example (5, 0). On the y-axis, x = 0: for example (0, −3).
Pause and explainWhere would (−3, 2) lie relative to the origin?
Three units left and two units up. Its negative x-coordinate changes the horizontal direction only.
Read a diagram accurately
Reading a plotted point reverses the process of plotting it. Trace from the point to each axis and read the values using that axis’s scale, rather than counting unlabelled grid squares as units.
A point on the x-axis has no vertical displacement, so its y-coordinate is zero. A point on the y-axis has x-coordinate zero. These simple cases are useful checks when naming intercepts and when deciding which coordinate changes along a horizontal or vertical line.
A rectangle has vertices (−2, 1), (4, 1) and (4, 5). Find the fourth vertex.
The missing vertex shares x = −2 with the left vertex and y = 5 with the top vertex.
Pause and explainWhat must the x-coordinate be for a point on the y-axis?
Zero. The point has not moved horizontally away from the y-axis.
Your turn. Keep the order.
Say each pair aloud as “x, then y” before plotting. Include negative signs and check the labelled grid scale on both axes.
After plotting a point, read it back as if someone else had drawn it. This catches swapped coordinates and movements in the wrong direction before they affect a larger graph.
Describe how to plot (−3, −5) from the origin, and name its quadrant.
Reveal worked answer
A point lies on the y-axis, 4 units below the origin. Give its coordinates.
Reveal worked answer
Three vertices of an axis-aligned rectangle are (−1, −2), (5, −2) and (5, 3). Find the fourth.