Definitions for all Transformations

Invariant:A point or a set of points are invariant under a transformation if it remains unchanged by the transformation.

Isometry: An isometry is a transformation where the size and shape of an image remain the same as the object. The object and the image are congruent.

Indirect (or opposite): An indirect transformation is one in which the sense or direction of the image is changed.


e.g. If Y10_Reflection_01.gifABC maps to Y10_Reflection_01.gifA´B´C´ under a transformation N.

Angle size and length are invariant.

Transformation N is an isometry.

N is an indirect transformation.



Location of Mirror Line

Orakei_Basin_Reflection.JPGA reflection is defined if the position of the mirror line or the position of a point and its image are known.The mirror line is the line at right angles to the line joining a point and its image.


M is a reflection in mirror line m.

M: A Y10_Reflection_03.gifA´ or M(A) = A´

means A maps to A´ or A´ is the image of A.


Properties of Reflection

Triangle PQR maps to triangle P´Q´R´ Y10_Reflection_04.gif

The object is the same distance in front of the mirror line m as the image is behind it. i.e. PT = P´ T

Length, angle size and area are invariant. i.e.

Length PQ = Length P´Q´

Y10_Reflection_05.gifPQR = Y10_Reflection_05.gif P´Q´R´

Area Y10_Reflection_01.gifPQR = Area Y10_Reflection_01.gifP´Q´R´

Any point on the mirror line is invariant.

i.e. S Y10_Reflection_03.gif S´

Reflection is an indirect transformation.

i.e. PQR is anti-clockwise.

P´Q´R´ is clockwise.

A line and its image will meet on the mirror line (unless the line is parallel to the mirror line).

i.e. Line PR and line P´R´ meet at V.

Reflection is an isometry.

i.e. Y10_Reflection_01.gifPQR andY10_Reflection_01.gifP´Q´R´ are congruent.

See examples of reflections − button_animation.gif

Location of Mirror Line


To find the mirror line given a line and its image:

1. Join the point and its image with a line.

2. Draw the perpendicular bisector of this line.
i.e. Halfway, and at right angles.

lineY10_Reflection_06.gifimage of line


Download an interactive spreadsheet (Microsoft Excel) showing reflections, rotations, translations and enlargements.


(Windows users, right click and "Save target as..." to save the files on your computer.)