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

The general rule for a rotation of $R_{0,90^{\circ}}$ about the origin $(0,0)$ for a point $(x,y)$ is $(x,y)\to(-y,x)$. For $R_{0,180^{\circ}}$: $(x,y)\to(-x,-y)$. For $R_{0,270^{\circ}}$: $(x,y)\to(y, - x)$. For $R_{0,- 90^{\circ}}$: $(x,y)\to(y,-x)$. For $R_{0,-180^{\circ}}$: $(x,y)\to(-x,-y)$.

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

For $R_{0,270^{\circ}}$: If $(x = 0,y = 5)$, then $(x,y)\to(y,-x)=(5,0)$.
For $R_{0,-90^{\circ}}$: If $(x = 0,y = 5)$, then $(x,y)\to(y,-x)=(5,0)$.

Answer:

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