Question

1. which transformation will carry the figure onto itself. choose all that apply. a. reflection across the y - axis b. rotation 90° clockwise about the origin c. reflection across the line y = 1 d. rotation 270° clockwise about the origin

Explanation:

Step1: Analyze reflection across y - axis

A reflection across the y - axis changes the sign of the x - coordinates of the vertices of the square. Since the square is symmetric about the y - axis, this transformation will carry the figure onto itself.

Step2: Analyze 90 - degree clockwise rotation

A 90 - degree clockwise rotation about the origin changes the coordinates of a point \((x,y)\) to \((y, - x)\). This will not carry the square onto itself as the orientation will change.

Step3: Analyze reflection across \(y = 1\)

The square is symmetric about the line \(y = 1\). Reflecting across the line \(y=1\) will carry the figure onto itself.

Step4: Analyze 270 - degree clockwise rotation

A 270 - degree clockwise rotation about the origin is equivalent to a 90 - degree counter - clockwise rotation. It changes the coordinates of a point \((x,y)\) to \((-y,x)\). This will not carry the square onto itself as the orientation will change.

Answer:

A. reflection across the y - axis, C. reflection across the line \(y = 1\)