ACARA v9 CONTENT DESCRIPTION “locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane”
Builds on: Cross-Sections and Right Prisms (AC9M6SP01). Describing objects in space leads to pinning down exact positions — here every point on a flat plane gets a precise address from two numbers.
The four quadrants
A Cartesian plane is built from two number lines crossing at right angles: a horizontal x-axis and a vertical y-axis, meeting at the origin. These axes divide the whole plane into four regions called quadrants, numbered one to four starting at the top right and going anticlockwise. Each quadrant is defined by the signs of its coordinates: the first has both positive, the second has negative x and positive y, and so on. Knowing the quadrants gives a quick sense of roughly where a point sits before its exact position is even read.
The four quadrants
The x and y axes divide the plane into four regions, numbered one to four.
Quadrant I holds points where x and y are (+, +) — the axes split the plane into four quadrants.
Naming a point
Every point on the plane is named by an ordered pair of numbers written in brackets, like the pair three and two. The first number is the x-coordinate, telling how far to move across from the origin; the second is the y-coordinate, telling how far to move up or down. The order matters, which is why it is called an ordered pair: the pair three and two is a different point from the pair two and three. This pairing gives every point a unique address, so any position on the plane can be named exactly and without confusion.
Plotting an ordered pair
A point is named by two numbers: how far across, then how far up or down.
Plot the point (3, 2). The x-coordinate moves across, the y-coordinate moves up or down.
Reading coordinates
Reading a point's coordinates reverses the plotting. Starting from a marked point, you trace straight back to each axis: across to the y-axis gives the x-coordinate, and down or up to the x-axis gives the y-coordinate. A point three to the right and two up is the pair three, two. The same care with order applies in reverse, so the across-value is always written first. Being able to read coordinates as fluently as plotting them is what makes the plane a two-way tool, turning positions into numbers and numbers back into positions.
Reading coordinates
Find how far across and how far up the point is. Across is x, up is y.
What are the coordinates of the marked point? Pick A, B or C.
Moving a point
A point can be moved to a new position by sliding it across the plane, and its coordinates change to match. Moving a point to the right increases its x-coordinate; moving it up increases its y-coordinate. A point at the pair one, two moved three to the right lands at the pair four, two. Each unit of movement adds to or subtracts from one coordinate, so the new position can be worked out by arithmetic alone. Watching coordinates change as a point moves connects the picture of sliding across a grid to the numbers that describe it.
Moving a point
Sliding a point across the plane changes its coordinates in a predictable way.
Move the point 3 right. Watch how the coordinates change.
How coordinates change
The link between a move and its coordinate change follows a clear rule. Horizontal moves affect only the x-coordinate: right adds, left subtracts. Vertical moves affect only the y-coordinate: up adds, down subtracts. A move that is purely sideways leaves the y-coordinate untouched, and a move that is purely up or down leaves the x-coordinate alone. Describing how the coordinates of a point change when it is moved is the heart of this unit, because it ties the geometry of position to the arithmetic of the two numbers.
How coordinates change
Moving right or left changes x; moving up or down changes y.
A point moves 3 right. Which coordinate changes, and how?
Plotting a shape
Coordinates can pin down not just single points but whole shapes. Given a list of ordered pairs, plotting each point and joining them in order draws a polygon: four corners make a square or rectangle, three make a triangle. Because each corner has an exact coordinate, the shape can be drawn precisely and, just as importantly, described to someone else with nothing but a list of numbers. This is how the coordinate plane becomes a language for geometry, letting shapes be recorded, shared and moved entirely through their coordinates.
Plotting a shape
A list of coordinate pairs, joined in order, draws a shape on the plane.
Plotting (1, 1), (4, 1), (4, 4), (1, 4) and joining them in order draws a square — coordinates pin down a whole shape.
Where coordinates lead
The Cartesian plane is one of the most powerful ideas in mathematics, and locating points in all four quadrants is the first step into it. From here, coordinates carry transformations such as translations, reflections and rotations, the plotting of straight lines and graphs, and eventually the meeting of algebra and geometry where equations become curves. The simple act of naming a point with two numbers, and tracking how those numbers change as the point moves, underlies all of that later work.
Quick self-check
1. In the coordinate pair (3, 5), which number is the x-coordinate?
2. A point with coordinates (-2, 4) lies in which quadrant?
3. The point (-3, -1) has...
4. A point at (2, 3) moves 4 right. What are its new coordinates?
5. A point moves 3 down. Which coordinate changes?