Respuesta :
General Idea:
Reflection Rules:
The reflection of the point (x,y) across the x-axis is the point (x,-y).
The reflection of the point (x,y) across the y-axis is the point (-x,y).
Rotation Rules:
The 90 degree counterclockwise rotation about the origin of a point (x, y) is the point (-y, x)
The 180 degree counterclockwise rotation about the origin of a point (x, y) is the point (-x, -y)
The 270 degree counterclockwise rotation about the origin of a point (x, y) is the point (y, -x)
The 90 degree clockwise rotation about the origin of a point (x, y) is the point (y, -x)
The 180 degree clockwise rotation about the origin of a point (x, y) is the point (-x, -y)
The 270 degree clockwise rotation about the origin of a point (x, y) is the point (-y, x)
Applying the concept:
Let us consider any one of the vertices of the triangle. Let J is given by the point (x, y).
(x, y) becomes (y, -x) after performing a 90 clockwise rotation about the origin and then reflecting that point over the y-axis, we get J'(-y, -x)
We basically need to UNDO what we did to get the point J'(-y, -x) so that we can get it back J(x, y) .
We need to decide on what transformations to be done to J'(-y,-x) so that we get J(x, y)
Conclusion:
If we reflect the point (-y, -x) across the x-axis, then we get (-y, x),
And if we do 90 degree clockwise rotation to the point (-y, x), then we will get back to (x, y)
Option C is the right answer.
The transformation "a reflection over the x-axis and then a 90 clockwise rotation about the origin" will map J'K'L' back to JKL.
Answer:
The correct option is C.
Step-by-step explanation:
It is given that triangle JKL is transformed by performing a 90 clockwise rotation about the origin and then a reflection over the y-axis, creating triangle J’’K’’L’’.
If triangle JKL is transformed by performing a 90 clockwise rotation about the origin, then
[tex]J(x,y)\rightarrow J'(y,-x)[/tex]
After that it reflect over the y-axis.
[tex]J'(y,-x)\rightarrow J''(-y,-x)[/tex]
In option A:
A reflection over the y-axis and then a 90 clockwise rotation about the origin.
[tex]J''(-y,-x)\rightarrow J'''(y,-x)\rightarrow J''''(-x,-y)\neq J(x,y)[/tex]
Therefore, option A is incorrect.
In option B:
A reflection over the x-axis and then a 90 counterclockwise rotation about the origin
[tex]J''(-y,-x)\rightarrow J'''(-y,x)\rightarrow J''''(-x,-y)\neq J(x,y)[/tex]
Therefore, option B is incorrect.
In option C:
A reflection over the x-axis and then a 90 clockwise rotation about the origin.
[tex]J''(-y,-x)\rightarrow J'''(-y,x)\rightarrow J''''(x,y)=J(x,y)[/tex]
Therefore, option C is correct.
In option D:
A a reflection over the x-axis and then a reflection over the y-axis.
[tex]J''(-y,-x)\rightarrow J'''(-y,x)\rightarrow J''''(y,x)\neq J(x,y)[/tex]
Therefore, option D is incorrect.
