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 rule for rotating a point $(x,y)$ counter - clockwise about the origin by $90^{\circ}$ is $(x,y)\to(-y,x)$. By $180^{\circ}$ is $(x,y)\to(-x,-y)$. By $270^{\circ}$ is $(x,y)\to(y, - x)$.

Step2: Analyze the given points

The original point is $(0,5)$ and the new point is $(5,0)$.
For a $270^{\circ}$ counter - clockwise rotation ($R_{0,270^{\circ}}$) of the point $(0,5)$: Using the rule $(x,y)\to(y, - x)$, when $x = 0$ and $y = 5$, we get $(5,0)$.
For a $90^{\circ}$ clockwise rotation ($R_{0,-90^{\circ}}$), since clockwise rotation is the same as negative counter - clockwise rotation. The rule for a $90^{\circ}$ clockwise rotation of a point $(x,y)$ about the origin is also $(x,y)\to(y, - x)$. When $x = 0$ and $y = 5$, we get $(5,0)$.

Answer:

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