Question

y-axis to form △abc, and then △abc can be rotated 90° clock about the origin to form △abc.
true
false
△abc can be rotated 90° counterclockwise about the origin to form △abc, and then △abc can be dilated by a scale factor of 2 with the center of dilation at the origin to form △abc.
choose...

Explanation:

To determine if the statement is true or false, we analyze the transformations:

Step 1: Analyze the Rotation

A \( 90^\circ \) counterclockwise rotation about the origin transforms a point \( (x, y) \) to \( (-y, x) \). This is a rigid transformation (preserves shape and size).

Step 2: Analyze the Dilation

Dilation by a scale factor of 2 about the origin multiplies the coordinates of each point by 2 (e.g., \( (x, y) \to (2x, 2y) \)). This changes the size but preserves the shape (similarity transformation).

For the statement to be true, the sequence of rotation then dilation must map \( \triangle ABC \) to \( \triangle A''B''C'' \). Since rotation (rigid) and dilation (similarity) are valid transformations, if the resulting triangle after rotation and dilation matches \( \triangle A''B''C'' \), the statement is true. However, without specific coordinates for \( \triangle ABC \), \( \triangle A'B'C' \), and \( \triangle A''B''C'' \), we assume the context implies the transformations are valid. Typically, such problems structure the transformations to be consistent, so the statement is True (assuming the coordinate mappings align).

Answer:

True