Question

# Find the measure of the acute or right angle formed by intersecting lines so that C can be mapped to C' using two reflections. The rotation (x, y)→(y, -x) maps C to C'.

Solution

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The rotation $(x,y) \rightarrow (y,-x)$ is a 270$\text{\textdegree}$ counterclockwise rotation, that is equivalent to 90$\text{\textdegree}$ clockwise rotation,

The reflection on intersecting lines theorem considers the acute or right angel of the intersecting lines.

So, We will consider that the rotation is 90$\text{\textdegree}$ clockwise.

The angle of intersection is 45$\text{\textdegree}$

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