A reflection is fully stated if we know the mirror line. As with other transformations, we may be expected to use a mirror line to “do” a reflection, or to identify the mirror line that would cause a given reflection.

• Properties of reflection
  • A point and its image are equidistant from the mirror line;
  • The mirror line bisects the line joining a point and its image at right angles;
  • A line segment and its image are equal in length;
  • A line and its image are equally inclined to the mirror line;
  • Points on the mirror line and their images are the sames;
  • The image of a reflected object is congruent to it.

Worked Example

In the diagram below, reflect the triangle ABC about the mirror line.

Worked Example 2

Find the equation of the mirror line that takes object A below to image A’

Worked Example 3

In the diagram below, shape A is the object.

(a) Reflect shape A in the y axis. Label the image B.

(b) Reflect shape A and shape B in the x axis. Label the images A’ and B’ respectively.

Exercise

Answers