Question

Which shows the image of rectangle ABCD after the rotation (x, y) → (–y, x)? On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 2), B prime (0, negative 1), C prime (negative 4, negative 1), D prime (negative 4, negative 2). On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (1, negative 1), B prime (0, negative 1), C prime (0, negative 5), D prime (1, negative 5). On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 3), B prime (0, negative 1), C prime (negative 4, negative 2), D prime (negative 4, negative 3). On a coordinate plane, 2 rectangles are shown. The first rectangle has points A (negative 2, 0), B (negative 1, 0), C (negative 1, 4), D (negative 2, 4). The second rectangle has points A prime (0, negative 2), B prime (0, negative 1), C prime (4, negative 1), D prime (4, negative 2).

Answer 1

Answer

A on ed 2020

Step-by-step explanation:

Answer 2

The image of the rectangle ABCD is the rectangle that has points

A' (0 , -2) , B' (0 , -1) , C' (-4 , -1) and D' (-4 , -2) ⇒ 1st answer

Step-by-step explanation:

Let us revise the cases of rotation

1. If point (x , y) rotated about the origin by angle 90° anti-clock wise

  then its image is (-y , x)

2. If point (x , y) rotated about the origin by angle 180° anti-clock wise

  then its image is (-x , -y)

3. If point (x , y) rotated about the origin by angle 270° anti-clock wise

  then its image is (y , -x)

4. If point (x , y) rotated about the origin by angle 90° clock wise

    then its image is (y , -x)

5. If point (x , y) rotated about the origin by angle 180° clock wise

    then its image is (-x , -y)

6. If point (x , y) rotated about the origin by angle 270° clock wise

    then its image is (-y , x)

V.I.Note:  There is no difference between rotating 180° clockwise

or anti-clockwise around the origin

In rectangle ABCD,

∵ A = (-2 , 0)

∵ B = (-1 , 0)

∵ C = (-1 , 4)

∵ D = (-2 , 4)

∵ Rectangle ABCD is rotated by the rule (x , y) → (-y , x)

- That means 90° anti-clockwise about the origin

To find the image of each vertex change the sign of the y-coordinates

and switch x and y

∵ x-coordinate of point A = -2 and y-coordinate of point A = 0

∴ A' = (0 , -2)

∵ x-coordinate of point B = -1 and y-coordinate of point B = 0

∴ B' = (0 , -1)

∵ x-coordinate of point C = -1 and y-coordinate of point C = 4

∴ C' = (-4 , -1)

∵ x-coordinate of point D = -2 and y-coordinate of point D = 4

∴ D' = (-4 , -2)

The image of the rectangle ABCD is the rectangle that has points

A' (0 , -2) , B' (0 , -1) , C' (-4 , -1) and D' (-4 , -2)

Learn more:

You can learn more about rotation in brainly.com/question/9720317

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