Answer: the correct option is
(D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.
Step-by-step explanation: We are given two triangles ABC and A'B'C' on the co-ordinate grid.
We are given to select the set of transformations is performed on triangle ABC to form triangle A’B’C’.
From the graph, we note that
the co-ordinate of the vertices of triangle ABC are A(-4, -1), B(-3, -1) and C(-4, -4).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(-1, 1), B'(-2, 1) and C'(-1, 4).
We know that if a point (x, y) is translated 5 units right, followed by a rotation of 180-degrees clockwise about the origin, then its new co-ordinates becomes
(x, y) ⇒ (-x-5, -y).
So, after these two transformations, the co-ordinates of the vertices of triangle ABC will become
A(-4, -1) ⇒ (4-5, 1) = (-1, 1),
B(-3, -1) ⇒ (3-5, 1) = (-2, 1)
and
C(-4, -4) ⇒ (4-5, 4) = (-1, 4).
The new co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.
Thus, the required set transformations is
A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.
Thus, option (D) is CORRECT.
