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).

Answer 1

Answer: The correct options are

R 0,90,

R 0,270,

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

Step-by-step 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.

Answer 2

Answer:

R 0,90,

R 0,270,

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

Step-by-step explanation: