Question

bastian was able to map quadrilateral opqr onto onml using a reflection and a dilation.

bastian concluded:
\i was able to map quadrilateral opqr onto quadrilateral onml using a sequence of rigid transformations and dilations, so the figures are similar.\

what error did bastian make in his conclusion?

choose 1 answer:
a bastian used a reflection, so the quadrilaterals arent similar.
b bastian used a dilation, so the quadrilaterals arent similar.
c there is no error. this is a correct conclusion.

Explanation:

To determine the error in Bastian's conclusion, we recall the definition of similar figures: Two figures are similar if one can be mapped onto the other using a sequence of rigid transformations (reflections, translations, rotations) and dilations. Reflections are rigid transformations (they preserve shape and size), and dilations preserve the shape (angles) while changing the size proportionally. So using a reflection and a dilation to map one quadrilateral to another is a valid way to show similarity.

• Option A is incorrect because reflections are rigid transformations and do not prevent similarity.
• Option B is incorrect because dilations are a key transformation for showing similarity (they create proportional scaling).
• Option C is correct because Bastian's conclusion is accurate: using a reflection (rigid) and dilation is a valid method to show the quadrilaterals are similar.

Answer:

C. There is no error. This is a correct conclusion.