# (02.02 mc) what set of reflections would carry rhombus abcd onto itself?

(02.02 mc) what set of reflections would carry rhombus abcd onto itself? y-axis, x-axis, y-axis x-axis, y-axis, y-axis y=x, x-axis, y=x, y-axis x-axis, y=x, x-axis, y=x

So for the rhombus to carry onto itself, it needs to start in one position and end up in that same position. In this case, (x,y) will need to end up on (x,y) after the reflections are done. Here what the options do:

A: y-axis, x-axis, y-axis

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

B: x-axis, y-axis, y-axis

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

C: y=x, x-axis, y=x, y-axis

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

D: x-axis, y=x, x-axis, y=x

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

The only option that starts as (x,y) and ends as (x,y) is C: y=x, x-axis, y=x, y-axis, therefore making that the correct answer. y=x, x-axis, y=x, y-axis

Step-by-step explanation:

A reflection across the line y=x will switch the x- and y-coordinates:

(x, y)→(y, x)

A reflection across the x-axis will negate the y-coordinate:

(y, x)→(y, -x)

A reflection across the line y=x will again switch the x- and y-coordinates:

(y, -x)→(-x, y)

A reflection across the y-axis will negate the x-coordinate:

(-x, y)→(x, y)

This is the same ordered pair we began with, so this is correct.