Question

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

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

Explanation:

Answer 2

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.