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Reflecting shapes

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Position and transformation

Reflecting shapes

A reflection flips a shape across a mirror line. Reflect in the x-axis and the shape lands the same distance below it ā€” like a building reflected in still water.

mirror lineoriginalreflection

The mirror line

A REFLECTION flips a shape across a MIRROR LINE. On a coordinate grid the mirror line is usually one of the axes: ā€¢ The x-axis is the HORIZONTAL axis. ā€¢ The y-axis is the VERTICAL axis. Every point of the image is the same distance from the mirror line as the matching point of the object ā€” just on the other side.

How to draw one

Work one vertex at a time. 1. Take a vertex of the object. 2. Measure how far it is from the mirror line. 3. Plot its reflection the same distance on the other side. 4. Repeat for every vertex, then join them up with a ruler. Do not try to flip the whole shape in one go ā€” that is where mistakes creep in.

What happens to the coordinates

Reflecting in the x-axis keeps x and flips the SIGN of y: (3, 2) ā†’ (3, āˆ’2) Reflecting in the y-axis keeps y and flips the sign of x: (3, 2) ā†’ (āˆ’3, 2) The axis you reflect in is the coordinate that STAYS the same.

Congruent, but the other way round

The object and its image are CONGRUENT ā€” the same shape and the same size. But a reflection also reverses the shape, the way writing looks backwards in a mirror. That is the difference between a reflection and a translation: a slide keeps the shape facing the same way, a flip does not.

Worked examples

Reflect (3, 2) in the x-axis

  1. The x-axis is horizontal, so x stays the same.
  2. The y-coordinate changes sign: 2 ā†’ āˆ’2.

Answer: (3, āˆ’2)

Reflect (3, 2) in the y-axis

  1. The y-axis is vertical, so y stays the same.
  2. The x-coordinate changes sign: 3 ā†’ āˆ’3.

Answer: (āˆ’3, 2)

Reflect (āˆ’4, 5) in the x-axis

  1. Keep x = āˆ’4.
  2. Flip y: 5 ā†’ āˆ’5.

Answer: (āˆ’4, āˆ’5)

Reflect (āˆ’4, 5) in the y-axis

  1. Keep y = 5.
  2. Flip x: āˆ’4 ā†’ 4.

Answer: (4, 5)

A point already on the x-axis

  1. (6, 0) sits on the mirror line itself.
  2. It is 0 away from the line, so it does not move.

Answer: (6, 0) ā€” unchanged

Which axis was the mirror line?

  1. (2, 7) became (2, āˆ’7).
  2. The x-coordinate stayed the same.

Answer: It was reflected in the x-axis

Where you see this in real life

  • AMBULANCE is written reversed on the front of the vehicle so it reads correctly in a driver's mirror.
  • Butterfly wings and most building facades are designed as reflections about a central line.

Key words

Reflect
flip a shape across a mirror line
Mirror line
the line a shape is reflected in
x-axis
the horizontal axis
y-axis
the vertical axis
Congruent
exactly the same shape and size
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