Answer:
Rotate triangle A about the point (1.5, -0.5) by 180°.
Step-by-step explanation:
Translating a figure by a vector means shifting it 3 units left along the x-axis and 1 unit up along the y-axis.
The translation rule can be expressed as:
(x, y) → [(x - 3), (y + 1)]
Based on the provided figure,
The coordinates of triangle A are A(1, -1), B(1, -4) and C(3, -4)
Post-translation, the new coordinates are A'(-2, 0), B'(-2, -3), C'(0, -3).
Next, applying a 180° rotation to these new points about the origin gives:
Rotation rule:
(x, y) → (-x, -y)
A'(-2, 0) → A"(2, 0)
B'(-2, -3) → B"(2, 3)
C'(0, -3) → C"(0, 3)
Thus, the transformation A(1, -1) → A"(2, 0) represents the entire transformation.
The rule defining the transformation mapping triangle C to A would be expressed as:
Rotate triangle A about the point (1.5, -0.5) by 180°.
