Question

The figure below shows two triangles on the coordinate grid: (pic attached)

Which set of transformations is performed on triangle ABC to form triangle A’B’C’?
A) A translation five units up, followed by a 270-degree counterclockwise rotation about the origin.
B) A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units up
C) A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units to the right
D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin

Answer 1

D) A translation 5 units to the right, followed by a 180-degree counterclockwise rotation about the origin.

Explanation:

Given is the graph of ABC and A'B'C'.

We can take reference of parallel lines AB and A'B', it means the shape is rotated 180 degrees counterclockwise.

For A'B'C' to be in third quadrant, its original shape must be in first quadrant. It means ABC should be translated to first quadrant.

Checking the given options, we can say ABC is translated 5 units to the right (towards first quadrant), followed by a 180 degree counterclockwise rotation about the origin (resulting in third quadrant).

Hence, option D is correct.