Question

The glide reflection that maps ΔDEF onto ΔD'E'F' is T º Ry = 1 where a = and b = .

A. a = -1, b = 0
B. a = 0, b = 1
C. a = 1, b = 0
D. a = 0, b = -1

Answer 1

The question lacks the necessary specific values of 'a' and 'b' to determine the glide reflection that maps ΔDEF onto ΔD'E'F'.

Step-by-step explanation:

The question seems to have some missing details that prevent a direct answer. Typically, in mathematics, when we talk about glide reflections, we are referring to a transformation that combines a translation with a reflection in a line parallel to the direction of the translation. The notation T ° Ry = 1 where a = and b = suggests a transformation composed of a reflection across a line y = ax + b followed by a translation. However, without the specific values of 'a' and 'b', it is impossible to determine which exact transformation will map ΔDEF onto ΔD'E'F'.

Answer 2

In this case, the glide reflection that maps ΔDEF onto ΔD'E'F' is T º Ry = 1 where a = 0 and b = -1.

Therefore, The answer is option D) a = 0, b = -1 i

Step-by-step explanation:

To determine the values of a and b in the glide reflection transformation T º Ry = 1, we need to understand the properties of glide reflections.

A glide reflection is a combination of a reflection and a translation. In this case, T represents a translation and Ry represents a reflection over the y-axis.

For a glide reflection to map ΔDEF onto ΔD'E'F', the translation T must move each point of ΔDEF in the same direction as the reflection Ry. Since the reflection Ry is over the y-axis, the translation T must also move the points in the y-direction.

Now let's consider the given options.

To determine the correct values of a and b, we need to identify the direction of the translation.

• Option A states that a = -1 and b = 0. This means the translation T moves the points of ΔDEF in the negative x-direction and does not move them in the y-direction. This contradicts the requirement of the glide reflection.

• Option B states that a = 0 and b = 1. This means the translation T does not move the points of ΔDEF in the x-direction and moves them in the positive y-direction. This aligns with the requirement of the glide reflection.

• Option C states that a = 1 and b = 0. This means the translation T moves the points of ΔDEF in the positive x-direction and does not move them in the y-direction. This contradicts the requirement of the glide reflection.

• Option D states that a = 0 and b = -1. This means the translation T does not move the points of ΔDEF in the x-direction and moves them in the negative y-direction. This aligns with the requirement of the glide reflection.

Based on the analysis, the correct values for a and b in the glide reflection transformation T º Ry = 1 are:

a = 0

b = -1

Therefore, option D is the correct answer.

Your question is incomplete, but most probably the full question was:

The figure shows ΔDEF and ΔD'E'F'. Fill in each entry box with the answer.

The glide reflection that maps ΔDEF onto ΔD'E'F' is T º Ry = 1 where a = ____ and b = ____