Mathematics: Instructions: select the correct answer. which sequence is not equivalent to the others? a reflection across the y-axis, followed by a reflection across the x-axis, and then a 90° clockwise rotation about the origin a 90° clockwise rotation about the origin and then a 180° rotation about the origin a reflection across the x-axis, followed by a 90° counterclockwise rotation about the origin, and then a reflection across the x-axis a 90° counterclockwise rotation about the origin nextreset

On what?Step-by-step explanation:...

Instructions: select the correct answer. which

keonburkes9

11.01.2022

The correct option is 3.

Step-by-step explanation:

Option 1,

A reflection across the y-axis,

$P(x,y)\rightarrow P_1(-x,y)$

then reflection across the x-axis

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

$P_1(-x,y)\rightarrow P_2(-x,-y)$

and then a 90° clockwise rotation about the origin.

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

$P_2(-x,-y)\rightarrow P_3(-y,x)$

So the image of P(x,y) is P'(-y,x).

Option 2,

A 90° clockwise rotation about the origin

$P(x,y)\rightarrow P_1(y,-x)$

and then a 180° rotation about the origin.

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

$P_1(y,-x)\rightarrow P_2(-y,x)$

So the image of P(x,y) is P'(-y,x).

Option 3,

A reflection across the x-axis,

$P(x,y)\rightarrow P_1(x,-y)$

Followed by a 90° counterclockwise rotation about the origin.

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

$P_1(x,-y)\rightarrow P_2(y,x)$

and then a reflection across the x-axis.

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

$P_2(y,x)\rightarrow P_3(y,-x)$

So the image of P(x,y) is P'(y,-x).

Option 4,

A 90° counterclockwise rotation about the origin

$P(x,y)\rightarrow P_1(-y,x)$

So the image of P(x,y) is P'(-y,x).

The third sequence is not equivalent to the others. Therefore the correct option is 3.

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