Question

which shows the image of δrst after the rotation (x, y) → (y, -x)?

Explanation:

Step1: Identify vertices of ΔRST

Let the coordinates of R, S, T be $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ respectively from the graph.

Step2: Apply rotation rule

For a point $(x,y)$ rotated as $(x,y)\to(y, - x)$, for vertex R with coordinates $(x_1,y_1)$ the new - coordinates will be $(y_1,-x_1)$, for vertex S with coordinates $(x_2,y_2)$ the new - coordinates will be $(y_2,-x_2)$ and for vertex T with coordinates $(x_3,y_3)$ the new - coordinates will be $(y_3,-x_3)$.

Step3: Plot new vertices

Plot the new vertices on the coordinate - plane to get the image of ΔRST.

Since the original graph is not accompanied by answer - choices, we cannot provide a specific final answer. But the general procedure to find the image of ΔRST after the given rotation is as above. If we assume the coordinates of R, S, T are found to be R(-2,1), S(2,3), T(0,6):
For R(-2,1): After rotation, the new point $R'$ has coordinates $(1,2)$.
For S(2,3): After rotation, the new point $S'$ has coordinates $(3, - 2)$.
For T(0,6): After rotation, the new point $T'$ has coordinates $(6,0)$. Then we can plot $R'$, $S'$, $T'$ to get the new triangle.

Answer:

Step1: Identify vertices of ΔRST

Let the coordinates of R, S, T be $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$ respectively from the graph.

Step2: Apply rotation rule

For a point $(x,y)$ rotated as $(x,y)\to(y, - x)$, for vertex R with coordinates $(x_1,y_1)$ the new - coordinates will be $(y_1,-x_1)$, for vertex S with coordinates $(x_2,y_2)$ the new - coordinates will be $(y_2,-x_2)$ and for vertex T with coordinates $(x_3,y_3)$ the new - coordinates will be $(y_3,-x_3)$.

Step3: Plot new vertices

Plot the new vertices on the coordinate - plane to get the image of ΔRST.

Since the original graph is not accompanied by answer - choices, we cannot provide a specific final answer. But the general procedure to find the image of ΔRST after the given rotation is as above. If we assume the coordinates of R, S, T are found to be R(-2,1), S(2,3), T(0,6):
For R(-2,1): After rotation, the new point $R'$ has coordinates $(1,2)$.
For S(2,3): After rotation, the new point $S'$ has coordinates $(3, - 2)$.
For T(0,6): After rotation, the new point $T'$ has coordinates $(6,0)$. Then we can plot $R'$, $S'$, $T'$ to get the new triangle.