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

90° counterclockwise rotation about point 0, then composition reflection across the x-axis  

Step-by-step explanation:

The composition of transformations is the performance of more than one transformation on a figure.

1. 90° counterclockwise rotation about the origin  

When we rotate a point (x,y) 90° counterclockwise about the origin, it becomes (-y,x).

The rule is (x,y) ⟶ (y,x).

The coordinates of ABC change as follows:

A(5,2) ⟶ A'(-2,5)

B(2,4) ⟶ B'(-4,2)

C(2,1) ⟶ C'(-1,2)

The coordinates of  the image triangle are:

A'(–2, 5), B'(–4, 2), C'(1, -2)

2. Composition reflection about x-axis

When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign.

The rule is

(x,y) ⟶ (x,-y)

Thus,

A'(-2,5) ⟶ A"(-2, -5)

B'(-4,2) ⟶ B"(-4, -2)

C'(-1,2) ⟶ C"(-1, -2)

The coordinates of  the image triangle are:

A"(–2, -5), B"(–4, 2), C"(1, -2)

The figure below shows the composition of the two transformations.

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