501 Geometry Questions

What Is a Translation?

A translationis a transformation that slides a point or object horizontally,
vertically, or in a diagonal shift. When a figure is translated, it will look
exactly the same, but will have a different location.
The notation Th,kis used to give translation instructions.The sub-
script hshows the movement that will be applied to the x-coordinate and the
subscript kshows the movement that will be applied to the y-coordinate.
These numbers are each added to the x-coordinate and y-coordinate in
the preimage.

Example: Translate V(4,–5) using translation T-2,4

Solution:Beginning with V(4,–5), add –2 to the x-coordinate and

add 4 to the y-coordinate: V(4,–5) would be V'(4 + –2), (–5 + 4) =

V'(2,–1). This translation is illustrated in the following figure.

x

y

V^1 (2,–1)

V(4,–5)

h = –2

k = 4

Point V(4,–5) is translated

using T–2,4 and becomes V^1 (2,–1)

501 Geometry Questions