Triangle xyz with vertices x(0, 0), y(0, –2), and z(–2, –2) is rotated to create the image triangle x'(0, 0), y'(2, 0), and z'(2, –2). which rules could describe the rotation? check all that apply. r0, 90° r0, 180° r0, 270° (x, y) → (–y, x) (x, y) → (y, –x)

The correct options are

(A) Rotation 90° anticlockwise.

(D)  (x, y) → (–y, x).

Step-by-step explanation:  Given that ΔXYZ is rotated to create the image triangle ΔX'Y'Z'.

Triangle XYZ and its image triangle X'Y'Z' are shown in the attached figure.

The co-ordinates of the vertices of ΔXYZ are X(0, 0), Y(0, -2) and Z(-2, -2).

And the co-ordinates of the vertices ΔX'Y'Z' are X'(0, 0), Y'(2, 0) and Z'(2, -2).

Option (A) Rotation 90°:

We see from the figure that if we rotate ΔXYZ is rotated 90° anticlockwise, then it will coincide with ΔX'Y'Z'.

So, rotation of 90° anticlockwise is a correct option.

Option (B) Rotation 180°:

If we rotate ΔXYZ is rotated clockwise or anticlockwise 180°, then it will NOT coincide with ΔX'Y'Z'.

So, rotation of 180° is NOT a correct option.

Option (C) Rotation 270°:

If we rotate ΔXYZ is rotated clockwise 270°, then also it will not coincide with ΔX'Y'Z'.

So, rotation of 270° clockwise is also a correct option.

Option (D) (x, y) → (–y, x):

We see that the co-ordinates of both the triangle follow the transformation

X(0, 0)   ⇒  X'(0, 0)

Y(0, -2)  ⇒   Y'(2, 0)

Z(-2, -2)  ⇒   Z'(2, -2).

So, the transformation is (x, y) ⇒  (-y, x).

Therefore, the  transformation (x, y) → (–y, x) is a correct option.

Option (E) (x, y) → (y, -x):

We see that the co-ordinates of both the triangle does NOT follow this transformation

For example, suppose this transformation is correct. Then, we have

Y(0, -2)  ⇒  (-2, 0), which are not the co-ordinates of Y'.

Therefore, the  transformation (x, y) → (–y, x) is NOT a correct option.

Thus, the correct options are:

(A) Rotation 90° anticlockwise.

(D)  (x, y) → (–y, x).

the correct answe is A and D. Just took the test on Edgeunity.

(x, y) → (–y, x)

Rotation by 90° around the origin in counterclockwise direction

Explanation:

In this problem, we hace the following vertices:

Each vertex is rotated to create the following image triangle:

As you can see, if you consider the point (x,y), if you swap the x- and y-coordinates and then multiply the new x-coordinate by -1, you get the coordinates of the created image. Then, the rule you follow is:

(x, y) → (–y, x)

or in other words:

Rotation by 90° around the origin in counterclockwise direction

R0, 90°

(x, y) → (–y, x)

Explanation:

The triangles are shown below

The answer is R0, 90° and (x , y) → (-y , x) ⇒1st and 4th

Step-by-step explanation:

* Lets revise the rotation rules

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

 (+90° or -270°)

∴ Its image is (-y , x)

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

 (-90° or +270°)

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

 (+180° or -180°)

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

  anti-clockwise around the origin

* Lets solve the problem

∵ Δ XYZ has vertices⇒ X (0 , 0) , Y (0 , -2) , Z (-2 , -2)

∵ Δ X'Y'Z' has vertices X' (0 , 0) , Y' (2 , 0) , Z' (2 , -2)

* From them

# Y = (0 , -2) and Y' = (2 , 0), that means the image is (-y , x)

# Z = (-2 , -2) and Z' = (2 , -2), that means the image is (-y , x)

∴ The rotation is around the origin with angle 90° anti-clockwise

V.I.N: Anti-clock wise means positive angle , clockwise means

negative angle (90° means anti-clockwise , -90° means clockwise)

∴ The answer is: R0, 90° and (x , y) → (-y , x)