Chapter 14.4, Problem 34WE

a.

To determine

To find: Half turn maps to $P\text{'}$ .

Answer to Problem 34WE

Half turn $(3,2)$ maps $P\text{'}$ to $P$ .

Explanation of Solution

Given:

A half-turnabout $(3,2)$ maps $P$ to $P\text{'}$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

  $H_O:P\text{'}\to P$

Hence,

Half turn $(3,2)$ maps $P\text{'}$ to $P$ .

b.

To determine

To find: Half turn maps to $(0,0)$ .

Answer to Problem 34WE

  $(0,0)$ maps to $(6,4)$ half turnabout $(3,2)$ .

Explanation of Solution

Given:

A half-turnabout $(3,2)$ maps $P$ to $P\text{'}$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

  $(0,0)$ maps to $(6,4)$ half turnabout $(3,2)$ .

  

Hence,

  $(0,0)$ maps to $(6,4)$ half turnabout $(3,2)$ .

c.

To determine

To find: Half turn maps to $(3,0)$ .

Answer to Problem 34WE

Half turn $(3,2)$ maps $P\text{'}$ to $P$ .

Explanation of Solution

Given:

A half-turnabout $(3,2)$ maps $P$ to $P\text{'}$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

  $(3,0)$ maps to $(3,4)$ half turnabout $(3,2)$ .

  

Hence,

  $(3,0)$ maps to $(3,4)$ half turnabout $(3,2)$ .

d.

To determine

To find: Half turn maps to $(1,4)$ .

Answer to Problem 34WE

  $(1,4)$ maps to $(5,0)$ half turnabout $(3,2)$ .

Explanation of Solution

Given:

A half-turnabout $(3,2)$ maps $P$ to $P\text{'}$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

  $(1,4)$ maps to $(5,0)$ half turnabout $(3,2)$ .

  

Hence,

  $(1,4)$ maps to $(5,0)$ half turnabout $(3,2)$ .

e.

To determine

To find: Half turn maps to $(-2,1)$ .

Answer to Problem 34WE

  $(-2,1)$ maps to $(8,3)$ half turnabout $(3,2)$ .

Explanation of Solution

Given:

A half-turnabout $(3,2)$ maps $P$ to $P\text{'}$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

  $(-2,1)$ maps to $(8,3)$ half turnabout $(3,2)$ .

  

Hence,

  $(-2,1)$ maps to $(8,3)$ half turnabout $(3,2)$ .

f.

To determine

To find: Half turn maps to $(x,y)$ .

Answer to Problem 34WE

  $(x,y)$ maps to $(-x,-y)$ half turnabout $(3,2)$ .

Explanation of Solution

Given:

A half-turnabout $(3,2)$ maps $P$ to $P\text{'}$ .

Concept Used:

A rotation is a transformation suggested by rotating a paddle wheel. When wheel stops, new position of a paddle referred as the image of initial position.

Calculation:

As per the given problem

  

  $(x,y)$ maps to $(-x,-y)$ half turnabout $(3,2)$ .

Hence,

  $(x,y)$ maps to $(-x,-y)$ half turnabout $(3,2)$ .