Question

On a coordinate plane, 3 triangles are shown. Triangle A B C has points (5, 2), (2, 4), (2, 1). Triangle A prime B prime C prime has points (negative 2, 5), (negative 4, 2), (negative 1, 2). Triangle A double-prime B double-prime C double-prime has points (negative 2, negative 5), (negative 4, negative 2), (negative 1, negative 2).
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?

90 degree rotation about point 0 composition reflection across the x-axis
Reflection across the x-axis composition 90 degree rotation about point 0
180 degree rotation about point 0 composition reflection across the x-axis
Reflection across the x-axis composition 180 degree rotation about point 0

Answer 1

Reflection across the x-axis composition 90° rotation about the origin.

Reason: (x,y) → (-y,x) (a 90° CCW rotation about the origin) sends (5,2),(2,4),(2,1) to (-2,5),(-4,2),(-1,2). Then reflecting across the x-axis (x,y) → (x,-y) sends those to (-2,-5),(-4,-2),(-1,-2).