HELPPPP!! Kim performed a transformation on rectangle ABCD to create rectangle A'B'C'D', as shown in the figure below:

Rectangles ABCD and A prime B prime C prime and D prime are shown. A is at negative 1, 2. B is at negative 1, 5. C is at negative 3, 5. D is at negative 3, 2. A prime is at 2, 1. B prime is at 5, 1. C prime is at 5, 3. D prime is at 2, 3.

What transformation did Kim perform to create rectangle A'B'C'D'?
Rotation of 270 degrees counterclockwise about the origin
Reflection across the line of symmetry of the figure
Reflection across the y‐axis
Rotation of 90 degrees counterclockwise about the origin

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Respuesta :

johnsologan17 johnsologan17 · Answer 1 · 2020-12-14T16:25:41+01:00

Answer:

Rotation of 270 degrees counterclockwise

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-12-09T11:36:31+01:00

Transformation involves changing the position of a shape.

The transformation on rectangle ABCD to A'B'C'D' is (a) rotation of 270 degrees counterclockwise

The coordinates of ABCD are given as:

[tex]\mathbf{A = (-1,2)}[/tex]

[tex]\mathbf{B = (-1,5)}[/tex]

[tex]\mathbf{C = (-3,5)}[/tex]

[tex]\mathbf{D = (-3,2)}[/tex]

The coordinates of A'B'C'D' are given as:

[tex]\mathbf{A' = (2,1)}[/tex]

[tex]\mathbf{B' = (5,1)}[/tex]

[tex]\mathbf{C' = (5,3)}[/tex]

[tex]\mathbf{D' = (2,3)}[/tex]

The transformation from ABCD to A'B'C'D is 270 degrees counterclockwise about the origin.

And the proof is as follows.

The rule of 270 degrees counterclockwise about the origin is:

[tex]\mathbf{(x,y) \to (-y,x)}[/tex]

By testing the given coordinates, we have:

[tex]\mathbf{(2,1) \to (-1,2)}[/tex] --- A

[tex]\mathbf{(5,1) \to (-1,5)}[/tex] --- B

[tex]\mathbf{(5,3) \to (-3,5)}[/tex] --- C

[tex]\mathbf{(2,3) \to (-3,2)}[/tex] --- D

Hence, the true option is (a)