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. □ r₀,90° □ r₀,180° □ r₀,270° □ r₀,-90° □ r₀,-270°

Explanation:

Step1: Recall rotation rules

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

• \(R_{0,90^{\circ}}\): \((x,y)\to(-y,x)\)
• \(R_{0,180^{\circ}}\): \((x,y)\to(-x,-y)\)
• \(R_{0,270^{\circ}}\): \((x,y)\to(y,-x)\)
• \(R_{0,- 90^{\circ}}\) (equivalent to \(R_{0,270^{\circ}}\)): \((x,y)\to(y,-x)\)
• \(R_{0,-270^{\circ}}\) (equivalent to \(R_{0,90^{\circ}}\)): \((x,y)\to(-y,x)\)

Step2: Apply rules to the point \((3,-2)\)

• For \(R_{0,90^{\circ}}\): \((3,-2)\to(2,3)\) (since \(-(-2) = 2\) and \(x = 3\) becomes the \(y\)-coordinate)
• For \(R_{0,-270^{\circ}}\) (same as \(R_{0,90^{\circ}}\)): \((3,-2)\to(2,3)\)

Answer:

\(R_{0,90^{\circ}}\), \(R_{0,-270^{\circ}}\)