Question

figure s is the result of a transformation on figure r. which transformation would accomplish this?
answer
a translation 3 units left and 1 unit up
a translation 3 units right and 1 unit down
a rotation 90° counterclockwise about the origin
a rotation 90° clockwise about the origin

Explanation:

Step1: Analyze translation

Translation moves the figure without rotation. If it were a translation, the orientation of the figure would remain the same. But here, the orientation has changed, so it's not a translation.

Step2: Analyze rotation

Rotation changes the orientation of the figure. A \(90^{\circ}\) clock - wise rotation about the origin changes the position of points \((x,y)\) to \((y, - x)\). By observing the general shape and position change from Figure \(R\) to Figure \(S\) (orientation change which is characteristic of rotation), and comparing with the properties of rotation (while translation would keep the same orientation), we can confirm it's a rotation.

Answer:

A rotation \(90^{\circ}\) clockwise about the origin.