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Triangle XYZ with vertices X(0,0) , Y(0,-2) , Z(-2,-2) is rotated to create the image triangle X’(0,0) , Y’(2,0) , Z’(2,-2).

Which rules could describe the rotation ?

[]R 0,90
[]R 0,180
[]R 0,270
[](x,y) -> (-y,x)
[](x,y) -> (y,-x)

User Scrittler
by
7.5k points

2 Answers

4 votes

Answer:

R 0,90,

R 0,270,

(x,y) -> (-y,x)

Explanation:

User Bright Lee
by
7.9k points
2 votes

Answer: The correct options are

R 0,90,

R 0,270,

(x,y) -> (-y,x)

Explanation:

In R 0,90,


(x,y)\rightarrow (-y,x)

Thus, If the triangle XYZ with vertices X(0,0) , Y(0,-2) , Z(-2,-2) is rotated 90° about origin,

Then its new coordinates are,


(0,0)\rightarrow (0,0)


(0,-2)\rightarrow (2,0)


(-2,-2)\rightarrow (-(-2),-2))

Thus, If X'Y'Z' is the transformed triangle the coordinates of the transformed figure,

X'(0,0) , Y’(2,0) , Z’(2,-2).

First Option is correct.

In R 0,180,


(x,y)\rightarrow (-x,-y)

Thus, If the triangle XYZ with vertices X(0,0) , Y(0,-2) , Z(-2,-2) is rotated 90° about origin,

Then its new coordinates are,


(0,0)\rightarrow (0,0)


(0,-2)\rightarrow (0,2)


(-2,-2)\rightarrow (2,2)

Thus, If X'Y'Z' is the transformed triangle the coordinates of the transformed figure,

X'(0,0) , Y’(0,2) , Z’(2, 2).

Second option is incorrect.

In R 0,270,


(x,y)\rightarrow (-y,x)

Thus, If the triangle XYZ with vertices X(0,0) , Y(0,-2) , Z(-2,-2) is rotated 90° about origin,

Then its new coordinates are,


(0,0)\rightarrow (0,0)


(0,-2)\rightarrow (2,0)


(-2,-2)\rightarrow (-(-2),-2))

Thus, If X'Y'Z' is the transformed triangle the coordinates of the transformed figure,

X'(0,0) , Y’(2,0) , Z’(2,-2).

Third Option is correct.

In (x,y) -> (-y,x)

The new coordinates are,


(0,0)\rightarrow (0,0)


(0,-2)\rightarrow (2,0)


(-2,-2)\rightarrow (-(-2),-2))

Thus, If X'Y'Z' is the transformed triangle the coordinates of the transformed figure,

X'(0,0) , Y’(2,0) , Z’(2,-2).

Fourth Option is correct.

In (x,y) -> (y,-x)

The new coordinates are,


(0,0)\rightarrow (0,0)


(0,-2)\rightarrow (-2,0)


(-2,-2)\rightarrow (-2,-(-2))

Thus, If X'Y'Z' is the transformed triangle the coordinates of the transformed figure,

X'(0,0) , Y’(2,0) , Z’(-2,2).

Fourth Option is incorrect.

User Tyler Hamsmith
by
7.5k points

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