Answer:
(1) Rotation of 90° counterclockwise about the origin (2) Translation 2 units right .
Step-by-step explanation:
We have been asked to determine a sequence of transformations that maps △ABC to △A′B′C'.
To map △ABC to △A′B′C′ first of all we have to rotate △ABC 90° counterclockwise (positive rotation) about the origin. After rotating △ABC 90° our new coordinates will be A(-3,-4), B(-3,-1) and C (-1,-2).
We can see that distance between A and origin is [tex]\sqrt{5}[/tex] and distance between A' and origin is also [tex]\sqrt{5}[/tex]. Distance between A and A' is [tex]\sqrt{10}[/tex], which forms a right triangle.
To map △ABC to △A′B′C′ completely we will translate our △A′B′C' 2 units right. After translation our coordinates will be A'(-1,-4), B'(-1,-1) and C'(1,-2).
Therefore, a sequence of transformations that maps △ABC to △A′B′C′ is (1) rotation of 90° counterclockwise about the origin and (2) translation 2 units right.
