Geometry and measuresGCSE / IGCSE

Reflections of shapes

Reflect vertices at equal perpendicular distances from a mirror line.

  • State the equation of the mirror line when describing a reflection.
  • The line joining a point to its image is perpendicular to the mirror and is bisected by it.
  • Size is unchanged; orientation reverses.

Example 1

Reflect triangle in the line . Draw and label the image.

  1. Use the mirror line

    The dashed construction segments meet the mirror at right angles. Each vertex and its image are equally far from it.

  2. Reflect each vertex

    Only the coordinate perpendicular to the mirror changes.

Original shape
Original shape ABC on an equal-scale coordinate grid.
Original and image
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.
OriginalImageConstruction

Example 2

Reflect triangle in the line . Draw and label the image.

  1. Use the mirror line

    The dashed construction segments meet the mirror at right angles. Each vertex and its image are equally far from it.

  2. Reflect each vertex

    For swap the coordinates.

Original shape
Original shape ABC on an equal-scale coordinate grid.
Original and image
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.
OriginalImageConstruction

Remember
Use corresponding vertices to check the whole shape, not just one side.

Your turn

Question 1

Reflect triangle in the line . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 2

Reflect triangle in the line . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 3

Reflect triangle in the line . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 4

Reflect triangle in the line . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

Question 5

Reflect triangle in the line . Give the image coordinates and sketch the image. The vertices are , and .

Original shape ABC on an equal-scale coordinate grid.
Check answer
Original shape ABC and transformed image A prime B prime C prime on an equal-scale coordinate grid.

Apply the same transformation to every vertex, then join the image vertices in order.

← All Geometry and measures cardsReport a mistake