Parallelogram ABCD is translated (x +3, y-2) and then rotated 90° about the origin in the
clockwise direction. Complete the table to show the
locations of A", B", C", and D" after both
transformations.
A
B
D
A(-5,1) A?
B(-4, 3) B?
C(-1,3) C?
D(-2, 1) D?
A" (-1, 2), B" (1, 1), C" (1, -2), D" (-1,-1)
OA" (1,-2), B" (-1,-1), C" (-1, 2), D" (1, 1)
OA" (-2, -1), B" (-1, 1), C" (2, 1), D" (1,-1)
OA" (1, 1), B" (-1, 2), C" (-1, -1), D" (1,-2)
9
9

To solve this problem, we'll perform two transformations on the parallelogram ABCD: a translation followed by a rotation.
Step 1: Translation
The translation given is ( x + 3 , y − 2 ) . Let's apply this translation to each vertex:

A :

Original coordinates: ( − 5 , 1 )
Translated coordinates: ( − 5 + 3 , 1 − 2 ) = ( − 2 , − 1 )


B :

Original coordinates: ( − 4 , 3 )
Translated coordinates: ( − 4 + 3 , 3 − 2 ) = ( − 1 , 1 )


C :

Original coordinates: ( − 1 , 3 )
Translated coordinates: ( − 1 + 3 , 3 − 2 ) = ( 2 , 1 )


D :

Original coordinates: ( − 2 , 1 )
Translated coordinates: ( − 2 + 3 , 1 − 2 ) = ( 1 , − 1 )



Step 2: Rotation
After translating, we rotate each point 90° clockwise about the origin. The rule for this transformation is ( x , y ) → ( y , − x ) .

A' (-2, -1) :

After rotation: ( − 1 , 2 )


B' (-1, 1) :

After rotation: ( 1 , 1 )


C' (2, 1) :

After rotation: ( 1 , − 2 )


D' (1, -1) :

After rotation: ( − 1 , − 1 )



Conclusion
The final locations after both transformations are:

A" (-1, 2)
B" (1, 1)
C" (1, -2)
D" (-1, -1)

Therefore, the correct choice from the given options is the first one:
A" (-1, 2), B" (1, 1), C" (1, -2), D" (-1, -1).

Answered by danjohnbrain | 2025-07-22