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Reflections

FoundationHigherAQAEdexcelOCR

Master reflections for GCSE Maths with structured, exam-style practice. This Foundation and Higher resource covers reflecting shapes in a mirror line and includes a complete mark scheme showing the steps examiners reward. Suitable for AQA, Edexcel and OCR. Free to download as a PDF. Each point and its image are the same distance from the mirror line.

Free downloads

These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A reflection flips a shape across a mirror line, producing a mirror image. Every point moves to the opposite side of the line, the same perpendicular distance away.

The mirror line must be given by its equation, such as \(y = 2\), \(x = -1\), \(y = x\) or \(y = -x\). Describing a reflection without naming the line is an incomplete answer.

Any point already on the mirror line does not move. That gives a useful check: if part of your shape touches the line, that part should be identical in the image.

Revision notes

Reflecting in horizontal and vertical lines

Count the perpendicular distance from each vertex to the line, then measure the same distance on the other side.

Reflecting \((3, 5)\) in \(y = 2\): the point is \(3\) above the line, so the image is \(3\) below, at \((3, -1)\).

Reflecting in y = x

Reflecting in \(y = x\) swaps the coordinates, so \((a, b)\) becomes \((b, a)\).

Reflecting in \(y = -x\) swaps them and changes both signs, so \((a, b)\) becomes \((-b, -a)\).

Describing a reflection

State that it is a reflection and give the equation of the mirror line.

The mirror line lies exactly halfway between each point and its image, which is how you find it from a diagram.

Key points

  • A reflection flips a shape across a mirror line.
  • Each point moves the same perpendicular distance to the other side.
  • Points on the mirror line do not move.
  • Reflecting in \(y = x\) swaps the coordinates.
  • The object and image are congruent.
  • Give the equation of the mirror line.

Worked examples

Example 1

Reflect the point \((4, 7)\) in the line \(y = 3\).

Working

\[7 - 3 = 4\]the point is 4 above the mirror line
\[3 - 4 = -1\]measure 4 below the line
\[(4, -1)\]state the image point

Example 2

Reflect the point \((2, 6)\) in the line \(y = x\).

Working

\[\text{Reflecting in } y = x \text{ swaps coordinates}\]apply the rule
\[(6, 2)\]state the image point

Example 3

Reflect the point \((5, 1)\) in the line \(x = 2\).

Working

\[5 - 2 = 3\]the point is 3 to the right of the line
\[2 - 3 = -1\]measure 3 to the left
\[(-1, 1)\]state the image point

Common mistakes

  • Not giving the equation of the mirror line.

    A full description names the transformation and the line.

  • Confusing \(x = 2\) with \(y = 2\).

    x = 2 is a vertical line; y = 2 is horizontal.

  • Measuring the distance incorrectly.

    The distance must be perpendicular to the mirror line.

  • Moving points that lie on the line.

    Points on the mirror line stay exactly where they are.

Exam tips

  • Count the perpendicular distance for each vertex separately.
  • Remember reflecting in y = x swaps the coordinates.
  • Check that any point on the line has not moved.
  • Always give the equation of the mirror line.

Key terms

Reflection
A flip across a mirror line.
Mirror line
The line a shape is reflected in.
Perpendicular
At right angles to.
Congruent
Identical in shape and size.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.