Question

observe the series of transformations below. what is the series of transformations shown above? rotation of 270° counterclockwise about the origin and a reflection of x = 0. rotation of 90° clockwise about the origin and a reflection across y = 0. rotation of 90° clockwise about the origin and a translation of 6 units down. rotation of 270° counterclockwise about the origin and a translation of 4 units down.

Explanation:

Step1: Analyze rotation

A $90^{\circ}$ clock - wise rotation about the origin changes the coordinates $(x,y)$ of a point to $(y, - x)$. Visually, the orientation of the triangle changes in a way consistent with a $90^{\circ}$ clock - wise rotation.

Step2: Analyze second transformation

After the rotation, the triangle is moved downwards. There is no reflection as the orientation of the triangle relative to the x - axis and y - axis is not flipped across a line. Counting the grid units, it is translated 6 units down.

Answer:

Rotation of $90^{\circ}$ clockwise about the origin and a translation of 6 units down.