Sheet № 157 · Foundation + Higher · AQA · Edexcel · OCR
Reflections –
Reflections are one of the four transformations you need to know for GCSE Maths. A reflection flips a shape over a mirror line so that the image is the same distance from the line as the original, on the opposite side. This guide covers reflecting in the axes, the lines y = x and y = −x, and other lines, with step-by-step methods for both
§Key definitions
Question:
Reflect the triangle with vertices A(1, 3), B(4, 3), and C(4, 1) in the x-axis.
Answer:
The image has vertices A'(1, −3), B'(4, −3), C'(4, −1).
Q1 (Foundation):
Reflect the point (5, 2) in the y-axis.
Q2 (Foundation):
Reflect the point (3, −4) in the x-axis.
Q3 (Higher):
A shape is reflected so that the point (1, 6) maps to (6, 1). What is the mirror line?
§Formulas to memorise
Reflection in the x-axis: (x, y) maps to (x, −y)
Reflection in the y-axis: (x, y) maps to (−x, y)
Reflection in y = x: (x, y) maps to (y, x)
Reflection in y = −x: (x, y) maps to (−y, −x)
Draw the mirror line — on the coordinate grid if it is not already shown.
For each vertex — of the shape, count the perpendicular distance from the vertex to the mirror line.
Plot the reflected vertex — the same distance on the other side of the line.
Connect — the reflected vertices to form the image.
Label the image — with dashed lines or primes (A', B', C') to distinguish it from the original.
Worked example
Reflect the triangle with vertices A(1, 3), B(4, 3), and C(4, 1) in the x-axis.
Working:
⚠ Common mistakes
- ✗Not describing the transformation fully. You must state the type of transformation (reflection) and the equation of the mirror line. Saying just "reflection" without the line loses marks.
- ✗Counting diagonally instead of perpendicularly. Always measure the shortest (perpendicular) distance from each point to the mirror line.
- ✗Confusing reflection with rotation. A reflected shape is a mirror image — it appears "flipped". A rotated shape keeps the same orientation.
✦ Exam tips
- →When describing a reflection, always write: "Reflection in the line [equation]." Both parts are needed for full marks.
- →To find the mirror line when given the object and image, find the midpoint of each pair of corresponding points — the mirror line passes through all midpoints.
- →Use tracing paper in the exam to check your reflection is accurate.
- →Reflections do not change the size or shape of the figure — the object and image are congruent.