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.

Parallelogram ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 1, 3. D is at negative 2, 1.

A (− 5, 1) A″ ?
B (−4, 3) B″ ?
C (−2, 3) C″ ?
D (−1, 1) D″ ?

A″ (−1, 2), B″ (1, 1), C″ (1, −2), D″ (−1, −1)
A″ (1, −2), B″ (−1, −1), C″ (−1, 2), D″ (1, 1)
A″ (−2, −1), B″ (−1, 1), C″ (2, 1), D″ (1, −1)
A″ (1, 1), B″ (−1, 2), C″ (−1, −1), D″ (1, −2)

A rotation of 90 degrees clockwise states that the x coordinate of the pre-image will be the -y coordinate of the new image, and that the y coordinate of the pre-image will be the x coordinate of the new image.

So the final coordinates of the parallelogram will be as stated:

A"=(-1,2)

B"=(1,1)

C"=(1,-2)

D"=(-1,-1)

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saimaparvezVT saimaparvezVT · Answer 2 · 2022-07-21T11:59:42+02:00

Final coordinates of the parallelogram will be A"=(-1,2), B"=(1,1), C"=(1,-2), D"=(-1,-1) which is correct option(A).

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The original coordinates are given

A (− 5, 1)

B (−4, 3)

C (−2, 3)

D (−1, 1)

Parallelogram ABCD is translated (x + 3, y − 2)

So, (x + 3, y - 2)

A"= (-2,-1)

B"=(-1,1)

C"=(2,1)

D"=(1,-1)

Parallelogram ABCD is translated rotated 90° about the origin in the clockwise direction,

A rotation of 90° clockwise states that the x coordinate of the pre-image will be the -y coordinate of the new image, and that the y coordinate of the pre-image will be the x coordinate of the new image.

So the final coordinates of the parallelogram will be as stated:

A"=(-1,2)

B"=(1,1)

C"=(1,-2)

D"=(-1,-1)

Hence, final coordinates of the parallelogram will be A"=(-1,2), B"=(1,1), C"=(1,-2), D"=(-1,-1)

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