one vertex of a triangle is located at (0, 5) on a coordinate grid. after a transformation, the vertex is…

one vertex of a triangle is located at (0, 5) on a coordinate grid. after a transformation, the vertex is located at (5, 0). which transformations could have taken place? select two options. $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,-90^{circ}}$ $r_{0,-180^{circ}}$

one vertex of a triangle is located at (0, 5) on a coordinate grid. after a transformation, the vertex is located at (5, 0). which transformations could have taken place? select two options. $r_{0,90^{circ}}$ $r_{0,180^{circ}}$ $r_{0,270^{circ}}$ $r_{0,-90^{circ}}$ $r_{0,-180^{circ}}$

Answer

Explanation:

Step1: Recall rotation rules

For a point ((x,y)) rotated about the origin ((0,0)):

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

Step2: Apply rules to the point ((0,5))

  • For (R_{0,270^{\circ}}) or (R_{0,-90^{\circ}}): Substitute (x = 0) and (y=5) into ((x,y)\to(y,-x)) We get ((0,5)\to(5,0))

Answer:

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