one vertex of a polygon is located at (3, -2). after a rotation, the vertex is located at (2, 3). which…

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. $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,-90^{circ}}$ $r_{0,-270^{circ}}$

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. $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,-90^{circ}}$ $r_{0,-270^{circ}}$

Answer

Answer:

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

Explanation:

Step1: Recall rotation rules

The rule for a $90^{\circ}$ counter - clockwise rotation ($R_{0,90^{\circ}}$) about the origin $(x,y)\to(-y,x)$. For the point $(3,-2)$, applying this rule gives $-(-2),3=(2,3)$.

Step2: Recall equivalent rotations

A $-270^{\circ}$ rotation is equivalent to a $90^{\circ}$ counter - clockwise rotation. A negative rotation is clockwise. Since $360 - 270=90$, a $R_{0,-270^{\circ}}$ rotation of the point $(3, - 2)$ about the origin also results in the point $(2,3)$.