Chapter 14.4, Problem 12CE

a.

To determine

To graph: $A(4,1)$ & origin & given coordinate of $H_o$

Answer to Problem 12CE

  $A(4,1)$ & origin is plot & coordinate of $H_o$ is $A(4,1)\to A\text{'}(-4,-1)$ .

Explanation of Solution

Given:

  $A(4,1)$ on a coordinate grid.

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

  $A(4,1)$ on a coordinate grid.

First draw the grid and Locate origin as well as point $A(4,1)$ in it.

Then rotate the point $A$ around the origin by ${180}^{°}$ to get the point $A\text{'}$ .

  

  $A(4,1)\to A\text{'}(-4,-1)$

Hence,

  $A(4,1)$ & origin is plot & coordinate of $H_o$ is $A(4,1)\to A\text{'}(-4,-1)$ .

b.

To determine

To graph: $R_{O,90}(A)$

Answer to Problem 12CE

Coordinate of $R_{O,90}(A)$ is $R_{O,90}:A(4,1)\to A\text{'}(-1,4)$ .

Explanation of Solution

Given:

  $A(4,1)$ on a coordinate grid.

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

  $A(4,1)$ on a coordinate grid.

To get the asked point, rotate the line $OA$ by ${90}^{°}$ counter-clockwise.

  

  $R_{O,90}:A(4,1)\to A\text{'}(-1,4)$

Hence,

Coordinate of $R_{O,90}(A)$ is $R_{O,90}:A(4,1)\to A\text{'}(-1,4)$ .

c.

To determine

To graph: $R_{O,-90}(A)$

Answer to Problem 12CE

Coordinate of $R_{O,-90}(A)$ is $R_{O,-90}:A(4,1)\to A\text{'}(1,-4)$ .

Explanation of Solution

Given:

  $A(4,1)$ on a coordinate grid.

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

  $A(4,1)$ on a coordinate grid.

To get the asked point, rotate the line clockwise $OA$ by ${90}^{°}$ .

  $A(4,1)\to A\text{'}(1,-4)$

Hence,

Coordinate of $R_{O,-90}(A)$ is $R_{O,-90}:A(4,1)\to A\text{'}(1,-4)$ .