Answer:
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.
