146k views
5 votes
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.

2 Answers

4 votes

Answer:

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

Explanation:

User James Danforth
by
8.0k points
4 votes

Answer: OPTION C.

Explanation:

It is important to know the following:

Dilation:

  • Transformation in which the image has the same shape as the pre-image, but the size changes.
  • Dilation preserves betweenness of points.
  • Angle measures do not change.

Translation:

  • Transformation in which the image is the same size and shape as the pre-image.
  • Translation preserves betweenness of points.
  • Angle measures do not change.

Therefore, since the Square T was translated and then dilated to create Square T'', we can conclude that the statement that explains why they are similar is:

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

User Skohrs
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories