Chapter 14.4, Problem 15CE

a.

To determine

To express: $R_K(A)=A\text{'}$

Answer to Problem 15CE

  $R_K(A)=A\text{'}$ is expressed as reflection of point $A$ over line $K$ is point $A\text{'}$ .

Explanation of Solution

Given:

  $R_K(A)=A\text{'}$

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

  $R_K(A)=A\text{'}$

Reflection of point $A$ over line $K$ is point $A\text{'}$ .

Hence,

  $R_K(A)=A\text{'}$ is expressed as reflection of point $A$ over line $K$ is point $A\text{'}$ .

b.

To determine

To express: $H_O:(-2,0)\to (2,0)$

Answer to Problem 15CE

  $H_O:(-2,0)\to (2,0)$ express as rotation about point $O$ about ${180}^{°}$ maps $(-2,0)$ to $(2,0)$ .

Explanation of Solution

Given:

  $H_O:(-2,0)\to (2,0)$

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

  $H_O:(-2,0)\to (2,0)$

Rotation about point $O$ about ${180}^{°}$ maps $(-2,0)$ to $(2,0)$ .

Hence,

  $H_O:(-2,0)\to (2,0)$ express as rotation about point $O$ about ${180}^{°}$ maps $(-2,0)$ to $(2,0)$ .

c.

To determine

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

Answer to Problem 15CE

  $T:(x,y)\to (x-1,y+3)$ is expressed as translation $T$ which maps point $(x,y)$ to point $(x-1,y+3)$ .

Explanation of Solution

Given:

  $T:(x,y)\to (x-1,y+3)$

Concept Used:

A translation is a transformation suggested by shifting or gliding. When stops, new position after shift referred as the image of initial position.

Calculation:

As per the given problem

  $T:(x,y)\to (x-1,y+3)$

Translation $T$ which maps point $(x,y)$ to point $(x-1,y+3)$ .

Hence,

  $T:(x,y)\to (x-1,y+3)$ is expressed as translation $T$ which maps point $(x,y)$ to point $(x-1,y+3)$ .

d.

To determine

To express: $R_{P,10}$

Answer to Problem 15CE

Explanation of Solution

Given:

  $R_{P,10}$

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

  $R_{P,10}$

Rotation for ${10}^{°}$ about point $P$ .

Hence,

  $R_{P,10}$ is expressed as rotation for ${10}^{°}$ about point $P$ .