A Years 6–7 foundation lesson that starts with ordered pairs and positive or negative movement, then extends to axes and simple reflections. Your class may meet these ideas in a different order; confidence with signed number lines is the useful starting point.
- Read or plot an ordered pair using the horizontal coordinate first and the vertical coordinate second.
- Use coordinate signs to distinguish the four quadrants, and recognise points on the axes.
- Reflect a point across a coordinate axis by changing the coordinate perpendicular to that axis.
The idea
An ordered pair locates a point relative to the origin, where the two axes meet. The first coordinate gives horizontal movement: positive right, negative left. The second gives vertical movement: positive up, negative down.
Before you begin: Read positive and negative integers on a number line.
Worked examples
01 Start with the method
Locate point P on the coordinate plane and name its quadrant.
Start at the origin. The first coordinate is −3, so move three units left along the horizontal axis.
The second coordinate is 2, so move two units up from that horizontal position.
The point is left of the vertical axis and above the horizontal axis. This is quadrant II.
A mistake to avoid
The order matters: (−3, 2) and (2, −3) are different points. A point on an axis is not inside any quadrant.
02Why coordinate order changes the point
Locate both points and identify their quadrants. Are they the same point?
For P, move four units left from the origin, then two units up. Negative x and positive y put it in quadrant II.
For Q, move two units right, then four units down. Positive x and negative y put it in quadrant IV.
The same two numbers in a different order give different horizontal and vertical positions.
03Reflecting a point that lies on an axis
Reflect R in the x-axis. Name the image and say whether either point is in a quadrant.
A zero horizontal coordinate places R on the y-axis, four units below the origin.
Reflection in the x-axis keeps the horizontal coordinate and reverses the vertical coordinate. The image is four units above the origin.
Both points have zero horizontal coordinate. They are on the y-axis, so neither is inside a quadrant.
Practice questions with answers
Work these out first, then open each solution to compare your method. These questions are untimed.
Question 1
Describe the movement from the origin and identify the axis.
Show solution 1
There is no horizontal movement. Move four units down; the point is on the negative vertical axis.
Question 2
Start at the origin, move three units right, then two units up. Write the coordinates.
Show solution 2
The horizontal movement gives the first coordinate and the vertical movement gives the second. Both are positive, so the point is in quadrant I.
Question 3
Which quadrant contains this point?
Show solution 3
A negative horizontal coordinate is left of the y-axis, and a negative vertical coordinate is below the x-axis. That region is quadrant III.
Question 4
Name the axis containing B. Does B belong to a quadrant?
Show solution 4
The vertical coordinate is zero, so B is on the horizontal axis, four units right of the origin. Axes form the boundaries between quadrants and are not inside them.
Question 5
Reflect C in the y-axis, then reflect that image in the x-axis. Give the final coordinates.
Show solution 5
The y-axis reflection changes the horizontal sign and keeps the vertical coordinate. The following x-axis reflection keeps the new horizontal coordinate and changes the vertical sign. The final point is in quadrant IV.
Common questions
Which coordinate comes first, and how are the quadrants numbered?
Write horizontal x first, then vertical y. Quadrant I is upper right; II is upper left; III is lower left; IV is lower right. The numbering goes anticlockwise from the upper right. A point on an axis or at the origin is not in a quadrant.
Why does reflecting in the x-axis change y rather than x?
The x-axis is horizontal. A reflection across it keeps the point’s left-to-right position, but puts it the same distance on the other side vertically. Reflecting in the vertical y-axis instead changes the horizontal coordinate and keeps the vertical one.