Geometry ! ! a sequence of transformations that maps △abc to △a′b′c′ a: (-4,3) b: (-1,3) c: (-2,1) a': (-1,-4) b': (-1,-1) c': (1,-2) pick two: rotation of 90° counterclockwise about the origin translation 2 units right reflection across the y - axis rotation of 180° about the origin

The correct answer is:

Rotation of 90° counterclockwise about the origin  and a translation 2 units right

Explanation:

A rotation 90° counterclockwise maps each point (x, y) to (-y, x).  This means our points would be:

A(-4,3)→(-3, 4); B(-1,3)→(-3, -1); C(-2,1)→(-1, -2)

A translation 2 units right will add 2 units to the new x-coordinates; this gives us

(-3, 4)→(-1, 4); (-3, -1)→(-1, -1); and (-1, -2)→(1, -2)

These are the points in the image, so this is the correct set of transformations.