Question

HELP PLEASE! Square T was translated by the rule (x + 2, y + 2) and then dilated from the origin by a scale factor of 3 to create square T″. Which statement explains why the squares are similar?


A. Translations and dilations preserve side length; therefore, the corresponding sides of squares T and T″ are congruent.


B. Translations and dilations preserve orientation; therefore, the corresponding angles of squares T and T″ are congruent.


C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.


D. Translations and dilations preserve collinearity; therefore, the corresponding angles of squares T and T″ are congruent.

Answer 1

The statement that explains why the squares are similar is

Option C. Translations and dilations preserve betweenness of points; therefore, the corresponding sides of squares T and T″ are proportional.

Further explanation

There are several types of transformations:

1. Translation
2. Reflection
3. Rotation
4. Dilation

Let us now tackle the problem!

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This problem is about Translation and Dilation.

Properties of Translation of the images compared to pre-images:

• preserve Side Length
• preserve Orientation
• preserve Collinearity
• preserve Betweenness of Points

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Properties of Dilation of the images compared to pre-images:

• not preserve Side Length
• not preserve Orientation
• preserve Collinearity
• preserve Betweenness of Points

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From the information above, we can conclude that:

Option A is not true because Dilations do not preserve side length.

Option B is not true because Dilations do not preserve orientation.

Option C is true because Translations and Dilations preserve betweenness of points.

Option D is not true. Although Translation and Dilations preserve collinearity but it cannot be related to the corresponding angles are congruent.

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Learn more

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Transformation

Keywords: Function , Trigonometric , Linear , Quadratic , Translation , Reflection , Rotation , Dilation , Graph , Vertex , Vertices , Triangle

Answer 2

Answer:

c

Step-by-step explanation: