Simplifying a Composition

Algebra Level 3

A figure is reflected first across the line $y=x$ and then across the line $y=-x$ . This composition is equivalent to which of the following single transformations?

reflection across the

y

-axis reflection across the

x

-axis rotation of

90^{\circ}

clockwise about the origin rotation of

180^{\circ}

about the origin rotation of

90^{\circ}

counterclockwise about the origin

1 solution

James Dohm
Jul 19, 2016

Considering the point $(a, b)$ :

Reflection Across $y=x$ : $(b, a)$

Reflection Across $y=-x$ : $(-a, -b)$

Simplifying a Composition

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