Answer:
Rotation of triangle A across a point (1.5, -0.5) by 180°.
Step-by-step explanation:
Translation of a figure about a vector means translation of a figure by 3 units to the left on x-axis and 1 unit in the positive direction of the y-axis.
Rule for the translation will be,
(x, y) → [(x - 3), (y + 1)]
From the figure attached,
Vertices of the triangle A are A(1, -1), B(1, -4) and C(3, -4)
After translation new image points will be A'(-2, 0), B'(-2, -3), C'(0, -3).
After rotation of these image points 180° about the origin will be,
Rule for the rotation,
(x, y) → (-x, -y)
A'(-2, 0) → A"(2, 0)
B'(-2, -3) → B"(2, 3)
C'(0, -3) → C"(0, 3)
Therefore, A(1, -1) → A"(2, 0) is the single transformation.
Rule for this transformation which maps triangle C to A will be defined by,
Rotation of triangle A across a point (1.5, -0.5) by 180°.
