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 ABC maps to A´B´C´ under a transformation N.
Angle size and length are invariant.
Transformation N is an isometry.
N is an indirect transformation.
M is a reflection in mirror line m.
M: A A´ or M(A) = A´
means A maps to A´ or A´ is the image of A.
Triangle PQR maps to triangle P´Q´R´
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´
PQR = P´Q´R´
Area PQR = Area P´Q´R´
Any point on the mirror line is invariant.
i.e. S 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. PQR andP´Q´R´ are congruent.
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.
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.)