501 Geometry Questions

What Is a Reflection?

A reflectionis a transformation that flips a point or object over a given
line. The shapeof the object will be the same, but it will be a mirror image
of itself. It is common that points, lines, or polygons will be reflected over
the x-axis or y-axis, but they can also be reflected over other lines as well
such as a diagonal. Polygon ABCD in preceding figure underwent a reflec-
tion over the y-axis to become A'B'C'D'. In order to reflect a point over
the y-axis, its y-coordinate stays the same, and its x-coordinate changes
signs. Here are the rules for reflections:

Point A(x,y) will become A'(–x,y) after being reflected over the y-axis.

Point B(x,y) will become B'(x,–y) after being reflected over the x-axis.

This figure demonstrates the reflection of point P over the x-axis.

y

x

As preimage P (–3,4) is reflected over

the x-axis, its image P ' becomes (–3,–4)

P (–3,4)

P '(–3,–4)

501 Geometry Questions