Question

What set of reflections would carry rhombus ABCD onto itself? Rhombus ABCD is shown. A is at 0, 2. B is at 1, 2. C is at 2, 4. D is at 3, 2. 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

Answer 1

What are your answer possibilities?

Answer 2

y=x, x-axis, y=x, y-axis

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.