Question

On a coordinate plane, 3 triangles are shown. Triangle A B C has points (5, negative 5), (1, negative 2), (1, negative 5). Triangle A prime B prime C prime has points (5, 5), (1, 2), (1, 5). Triangle A double-prime B double-prime C double prime has points (negative 1, 3), (negative 5, 0), (negative 5, 3).
Which rule describes the composition of transformations that maps ΔABC to ΔA"B"C"?

Translation of negative 6 units x, negative 2 units y composition reflection across the x-axis
Reflection across the x-axis composition translation of negative 6 units x, negative 2 units y
Translation of negative 6 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 translation of negative 6 units x, negative 2 units y

Answer 1

Answer: Translation of -6 units in x and -2 units in y composed with reflection across the x-axis.

Reason: Reflect ΔABC across the x-axis to get ΔA'B'C' (e.g. (5,-5) → (5,5)). Then translate by (-6, -2) (e.g. (5,5) → (-1,3)), which maps ΔA'B'C' to ΔA''B''C''. Thus the composition is: reflect across x-axis, then translate by (-6, -2).