Reflecting coordinates across the axes after PSLE is a useful way to connect signed numbers, symmetry and the coordinate plane before Secondary 1 graphs become more formal.
The wider route begins with After PSLE — Should My Child Start Secondary 1 Maths Early?. At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT.
The short answer: reflection changes one coordinate sign at a time
Reflecting a point across the y-axis reverses its horizontal position, so the x-coordinate changes sign while y stays the same.
Reflecting across the x-axis reverses the vertical position, so the y-coordinate changes sign while x stays the same.
Across the y-axis
The point (4, 3) reflects to (-4, 3). The distance from the y-axis is unchanged; only left and right reverse.
Across the x-axis
The point (4, 3) reflects to (4, -3). The distance from the x-axis is unchanged; only up and down reverse.
Through the origin
Reflecting through the origin reverses both directions, so (4, 3) becomes (-4, -3).
Why this is more than a sign trick
A reflection preserves distance from the mirror line. The sign change is simply the coordinate-language description of that geometric symmetry.
This makes the rule easier to remember than memorising “change x” or “change y” without seeing why.
Worked example: reflect (-5, 2)
Across the y-axis: (5, 2). Across the x-axis: (-5, -2). Through the origin: (5, -2).
Points on an axis may stay fixed
The point (0, 6) lies on the y-axis. Reflecting it across the y-axis leaves it at (0, 6) because its horizontal distance from that axis is zero.
Connect reflection to quadrants
A point in Quadrant I reflected across the y-axis moves to Quadrant II. Across the x-axis it moves to Quadrant IV. Through the origin it moves to Quadrant III.
For the wider coordinate foundation, read Coordinates and Graphs After PSLE.
A reflection routine
- Identify the mirror line.
- Decide which direction reverses.
- Change only the coordinate linked to that direction.
- Keep the distance from the mirror line unchanged.
- Plot the new point and check visually.
Independent practice with answers
- Reflect (3, 5) across the y-axis.
- Reflect (-4, 2) across the x-axis.
- Reflect (6, -1) through the origin.
- Reflect (0, 7) across the y-axis.
- Reflect (-2, -8) across the y-axis.
Answers: (-3,5); (-4,-2); (-6,1); (0,7); (2,-8).
Frequently asked questions
Why does reflecting across the y-axis change x?
Because the y-axis is vertical. Reflection across it reverses left and right, which is the x-direction.
Why review this after PSLE?
Because it joins signed numbers, coordinates and geometry in one simple visual relationship.
Return to the post-PSLE Mathematics hub or WhatsApp eduKatePunggol.
