Question

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)

Answer 1

R 0,90,

R 0,270,

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

Explanation:

Answer 2

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.