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Reflection in the x-axis

Cartesian plane shown with two triangles ABC and A' B' C'.
Detailed description

The point \(A\) in the diagram above has been reflected in the \(x\)-axis. To reflect \(A\), a line has been drawn at right angles to the axis of reflection (the \(x\)-axis in this case) and a ruler or compass has been used to mark \(A^\prime\) the same distance from the axis of reflection as \(A\), but on the other side. The same has been done for \(B\) and \(C\).

Using coordinates we can describe the reflection of the vertices:

\(A(1, 1) \rightarrow A^\prime (1, −1); B(4, 2) \rightarrow B^\prime (4, −2); C(2, 4) \rightarrow C^\prime (2, −4)\).

In general, \(P(x, y) \rightarrow P^\prime (x, −y)\).