91Ó°ÊÓ

Translation

In 2-dimensional geometry, a glide reflection is a symmetry operation that consists of a reflection over a line and then translation along that line, combined into a single operation.

As per the given problem

Translation $T:(x,y)→(x+3,y-1)$

Hence, x moves right 3 units & y moves 1 unit down.

Translation $T:(x,y)→(x+3,y-1)$

A translation moves ("slides") an object a fixed distance in a given direction without changing its size or shape, and without turning it or flipping it. The original object is called the pre-image, and the translation is called the image.

As per the given problem

Translation $T:(x,y)→(x+3,y-1)$

$T(4,6)→(4+3,6-1)=(7,5)$

Hence, the image of $(4,6)$ is $(7,5)$.

Translation $T:(x,y)→(x+3,y-1)$

A translation moves ("slides") an object a fixed distance in a given direction without changing its size or shape, and without turning it or flipping it. The original object is called the pre-image, and the translation is called the image.

As per the given problem

Translation $T:(x,y)→(x+3,y-1)$

$T^{-1}(x,y)→(x-3,y+1)$

$T^{-1}(2,3)→(2-3,3+1)=(-1,4)$

Hence, the preimage of $(2,3)$ is $(-1,4)$.