Question

question 8
a triangle is rotated 270 degrees counterclockwise about the origin to form its
image.
which statement correctly describes this transformation?
distances are preserved, but angle measure is not.
distances are not preserved, because the figure is turned.
distances are preserved, because rotations are rigid motions.
neither distance nor angles measure are preserved.
question 9

Explanation:

Step1: Recall properties of rotation

Rotation is a rigid motion. Rigid motions preserve distances (lengths of sides) and angle measures.

Step2: Analyze each option

• Option 1: "Distances are preserved, but angle measure is not." - Incorrect, as rotation (a rigid motion) preserves both.
• Option 2: "Distances are not preserved, because the figure is turned." - Incorrect, turning (rotating) does not change distances.
• Option 3: "Distances are preserved, because rotations are rigid motions." - Correct, as rigid motions (like rotation) keep distances (side - lengths) and angles the same.
• Option 4: "Neither distance nor angles measure are preserved." - Incorrect, rotation (a rigid motion) preserves both.

Answer:

"Distances are preserved, because rotations are rigid motions."