Question

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

Explanation:

Step1: Recall rotation rules about the origin

For a 90 - degree counter - clockwise rotation ($R_{0,90^{\circ}}$) of a point $(x,y)$ about the origin, the new point is $(-y,x)$. For a 180 - degree rotation ($R_{0,180^{\circ}}$) of a point $(x,y)$ about the origin, the new point is $(-x,-y)$. For a 270 - degree counter - clockwise rotation ($R_{0,270^{\circ}}$) of a point $(x,y)$ about the origin, the new point is $(y, - x)$. For a 90 - degree clockwise rotation ($R_{0,-90^{\circ}}$) of a point $(x,y)$ about the origin, the new point is $(y,-x)$. For a 180 - degree clockwise rotation ($R_{0,-180^{\circ}}$) of a point $(x,y)$ about the origin, the new point is $(-x,-y)$.

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

The original point is $(0,5)$.
For $R_{0,270^{\circ}}$: Let $x = 0$ and $y = 5$. The new point is $(y,-x)=(5,0)$.
For $R_{0,-90^{\circ}}$: Let $x = 0$ and $y = 5$. The new point is $(y,-x)=(5,0)$.

Answer:

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