Question

one vertex of a polygon is located at (3, -2). after a rotation, the vertex is located at (2, 3). which transformations could have taken place? select two options. consider both clockwise and counterclockwise rotations when answering this question. $r_{0, 90^{circ}}$ $r_{0, 180^{circ}}$ $r_{0, 270^{circ}}$ $r_{0, -90^{circ}}$ $r_{0, -270^{circ}}$

Explanation:

Step1: Recall rotation rules

For a point $(x,y)$ rotated about the origin:

• $R_{0,90^\circ}$ (counterclockwise 90°): $(x,y)\to(-y,x)$
• $R_{0,180^\circ}$ (180°): $(x,y)\to(-x,-y)$
• $R_{0,270^\circ}$ (counterclockwise 270° / clockwise 90°): $(x,y)\to(y,-x)$
• $R_{0,-90^\circ}$ (clockwise 90°): same as $R_{0,270^\circ}$
• $R_{0,-270^\circ}$ (clockwise -270° = counterclockwise 90°): same as $R_{0,90^\circ}$

Step2: Test $R_{0,90^\circ}$ on $(3,-2)$

Substitute into $(-y,x)$:
$(-(-2),3)=(2,3)$ → matches the new point.

Step3: Test $R_{0,-270^\circ}$ on $(3,-2)$

$R_{0,-270^\circ}$ is equivalent to counterclockwise 90°, so:
$(-(-2),3)=(2,3)$ → matches the new point.

Step4: Verify other options

• $R_{0,180^\circ}$: $(-3,2)$ → does not match
• $R_{0,270^\circ}$: $(-2,-3)$ → does not match
• $R_{0,-90^\circ}$: $(-2,-3)$ → does not match

Answer:

$R_{0, 90^\circ}$, $R_{0, -270^\circ}$