Chapter 14.3, Problem 1CE

a.

To determine

To find: $T$ glides point after translation?

Answer to Problem 1CE

  $T$ glides point 3 units right and 1 unit down.

Explanation of Solution

Given:

Translation $T:(x,y)\to (x+3,y-1)$

Concept Used:

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.

Calculation:

As per the given problem

Translation $T:(x,y)\to (x+3,y-1)$

Hence,

$x$ moves right 3 units & $y$ moves 1 unit down.

b.

To determine

To find:The image of $(4,6)$ ?

Answer to Problem 1CE

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

Explanation of Solution

Given:

Translation $T:(x,y)\to (x+3,y-1)$

Concept Used:

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.

Calculation:

As per the given problem

Translation $T:(x,y)\to (x+3,y-1)$

  $T(4,6)\to (4+3,6-1)=(7,5)$

Hence,

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

c.

To determine

To find:The preimage of $(2,3)$ ?

Answer to Problem 1CE

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

Explanation of Solution

Given:

Translation $T:(x,y)\to (x+3,y-1)$

Concept Used:

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.

Calculation:

As per the given problem

Translation $T:(x,y)\to (x+3,y-1)$

  $T^{-1}(x,y)\to (x-3,y+1)$

  $T^{-1}(2,3)\to (2-3,3+1)=(-1,4)$

Hence,

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