Question

Bobby drew a triangle on a coordinate grid, then rotated it 90 degrees clockwise, translated it 3 units to the right, and finally dilated it by a scale factor of 2. What is true about the two triangles that were created?

A. They are not similar but congruent.
B. They are not similar and not congruent.
C. They are similar but not congruent.
D. They are similar and congruent.

Answer 1

Bobby's transformed triangle is similar but not congruent to the original triangle, as its shape remains consistent, but its size is doubled.

Step-by-step explanation:

When considering the transformations applied to Bobby's triangle, we have a series of geometric operations. A 90-degree clockwise rotation does not change the size or shape of the triangle, meaning it remains similar to the original. The translation (moving the shape 3 units to the right) also does not change the shape or size, maintaining similarity. However, the dilation with a scale factor of 2 changes the size of the triangle but not its shape, which means the triangles remain similar because they have the same shape but are not congruent as they do not have the same size. Therefore, the correct answer to the question is C. They are similar but not congruent.