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Section 14.4 · Geometry and measure

Reflection

Reflect 2D shapes and points in a given mirror line on a coordinate grid, identify the mirror line, and recognise that the image is congruent to the object.

6 teaching slides 66 practice questions Worked answers for every question

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2 · Key words

reflectionA flip in a mirror line.
mirror lineThe line a shape is reflected in.
imageThe shape after the reflection.
congruentSame shape and same size.
invariant pointA point that does not move; here, one on the mirror line.
perpendicularAt right angles.

3 · Summary of the sectionrevise from this

  • A reflection flips a shape in a mirror line.
  • Every point and its image are the same distance from the mirror, on opposite sides, measured perpendicular to it.
  • Reflect in the x-axis: (x, y) → (x, −y).
  • Reflect in the y-axis: (x, y) → (−x, y).
  • Reflect in y = x: (x, y) → (y, x) — the coordinates swap.
  • A point on the mirror line does not move. It is invariant.
  • The image is congruent: every length and every angle is unchanged.
  • But the shape is turned over, so the vertices run the other way round.
  • To find an unknown mirror line, join a point to its image; the mirror cuts that join in half at right angles.
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Video lessons1 videos

Reflections

British corbettmaths

Reflecting in the axes and in other mirror lines, with the perpendicular-distance check.

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4 · Practice66 questions, easiest first

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14.3 Translation
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14.5 Rotation