Question

triangle would be
a different size than triangle abc
on the
coordinate grid. if she dilated triangle abc and then rotated it,
the resulting triangle would be
choose...
on the
coordinate grid.

Explanation:

To solve this, we analyze the transformations:

Step 1: Recall Dilation and Rotation Properties

• Dilation: Changes the size of a figure (scales it) but preserves shape (similarity).
• Rotation: A rigid transformation (like translation, reflection) that preserves size and shape (congruence), but dilation first changes the size.

Step 2: Analyze the Result of Dilation + Rotation

After dilating triangle \( ABC \) (which changes its size) and then rotating it, the resulting triangle will have a different size than a triangle formed by only rigid transformations (like rotation/reflection/translation, which preserve size). Since dilation is applied first, the size is altered, and rotation only changes orientation/position, not size (but the size was already changed by dilation).

Answer:

a different size than triangle \( A''B''C'' \) (assuming \( A''B''C'' \) is from rigid transformations; the key is dilation changes size, so the result of dilate + rotate is a different size than a non - dilated (rigid - transformed) triangle).