Chapter 8.8, Problem 4CFU

a.

To determine

To describe: the effects reflection, translation, and dilation have on the given situation by using a chart.

Answer to Problem 4CFU

Only reflection effects the figure’s orientation on the coordinate system by reflecting it over $xy,yz,\text{ or }xz$ plane.

Explanation of Solution

Given information:

Figure’s orientation on the coordinate system

Calculation:

The chart representing the effect of reflection, translation, and dilation on the figure’s orientation on the coordinate system is shown below.

Transformations	Orientation
Reflection	Yes
Translation	No
Dilation	No

Thus only reflection effects the figure’s orientation on the coordinate system. It reflects the figure over $xy,yz,\text{ or }xz$ plane.

b.

To determine

To describe: the effects reflection, translation, and dilation have on the given situation by using a chart.

Answer to Problem 4CFU

Only dilation effects the figure’s size by dilating it by the factor of $k$ (where $k\ne 0$ ).

Explanation of Solution

Given information:

Figure’s size

Calculation:

The chart representing the effect of reflection, translation, and dilation on the figure’s orientation on the coordinate system is shown below.

Transformations	Size
Reflection	No
Translation	No
Dilation	Yes

Thus only dilation affects the figure’s size by dilating it by the factor of $k$ (where $k\ne 0$ ).

c.

To determine

To describe: the effects reflection, translation, and dilation have on the given situation by using a chart.

Answer to Problem 4CFU

None of these affects the figure’s shape.

Explanation of Solution

Given information:

Figure’s shape

Calculation:

The chart representing the effect of reflection, translation, and dilation on the figure’s orientation on the coordinate system is shown below.

Transformations	Shape
Reflection	No
Translation	No
Dilation	No

Thus none of the given transformations affects the shape of figure.