Reflection: Mirror Lines on a Grid

G19Reflection

Flip it — a mirror image.

Reflection flips a shape over a mirror line; the image is reversed.

Reflect the flag in the y-axis.

Each point lands the same distance the OTHER side of the mirror line

Reflecting in the y-axis: (x, y) → (−x, y). In the x-axis: (x, y) → (x, −y).

Learn the 3-Step Method

1Find the mirror line.

It might be the y-axis, the x-axis, or any given line on the grid.

2Measure each point's distance.

Count squares from the point to the mirror — the image sits the SAME distance beyond it.

2 in → 2 out

3Flip, don't slide.

The image is reversed, like text in a mirror. (2, 4) reflected in the y-axis → (−2, 4).

(2,4) → (−2,4)

💡 Key IdeaPoints ON the mirror line don't move — they are their own reflection.

Worked Example

Reflect the point (3, 2) in the x-axis, then in the y-axis.

In the x-axis

y changes sign

(3, −2)

In the y-axis

x changes sign

(−3, 2)

✓ Remember

mirror in x-axis → flip y
mirror in y-axis → flip x

Watch Out! Common Mistakes

Sliding instead of flipping.

Not a translation! A reflection reverses the shape — if the image faces the same way, it’s wrong.

Wrong distance from the mirror.

Count carefully! A point 2 squares from the line lands exactly 2 squares beyond it — not 1, not 3.

Flipping the wrong coordinate.

(3, 2) in the x-axis → (−3, 2) ✕

Wrong axis! Reflecting in the x-axis flips y: (3, −2).

⬇ Cheat Sheet

REFLECTION

Find the mirror line first.
Each point lands the same distance the other side.
y-axis mirror: (x,y)→(−x,y). x-axis mirror: (x,y)→(x,−y).
Points on the mirror line stay put.

Example: (3, 2) → x-axis → (3, −2) · y-axis → (−3, 2).

📄 Free printable: Download the Reflection cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Reflection flips a shape over a mirror line, reversing it.
Each point lands the same distance on the other side of the line.
Mirror in the y-axis: (x, y) → (−x, y); in the x-axis: (x, y) → (x, −y).
Points on the mirror line don't move.

Frequently asked questions

What is a reflection in maths?

A transformation that flips a shape over a mirror line, producing a reversed image the same distance from the line on the other side.

What happens to coordinates when reflecting in the y-axis?

The x-coordinate changes sign and y stays the same: (3, 2) becomes (−3, 2).

How is reflection different from translation?

Translation slides the shape without changing its orientation; reflection flips it, so the image is reversed like writing in a mirror.

G20 Geometry Problem Solving

Reflection