Question

Which shows the image of ΔRST after the rotation (x, y) → (y, –x)?

On a coordinate plane, a triangle has points R (negative 2, 1), S (1, 3), T (negative 1, 8).

On a coordinate plane, a triangle has points R prime (1, 2), S prime (3, negative 1), T prime (7, 1).
On a coordinate plane, a triangle has points R prime (1, negative 2), S prime (3, 1), T prime (7, negative 1).
On a coordinate plane, a triangle has points R prime (negative 1, negative 2), S prime (negative 3, 1), T prime (negative 7, negative 1).
On a coordinate plane, a triangle has points R prime (2, 1), S prime (negative 1, 3), T prime (1, 7).

Answer 1

Apply (x,y) → (y,−x) to each vertex:

R(−2,1) → (1, −(−2)) = (1,2)
S(1,3) → (3, −1) = (3,−1)
T(−1,7) → (7, −(−1)) = (7,1)

So the matching image is the first option: R' (1,2), S' (3,−1), T' (7,1).

(If T were actually (−1,8) then T' would be (8,1), which is not among the choices.)