standard_description: Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, Ö3) lies on the circle centered at the origin and containing the point (0, 2).
problem_activity: Task
Below is a picture of a triangle on a coordinate grid:
[IMG]
Draw the reflection of $\triangle ABC$ over the line $x = -2$. Label
the image of $A$ as $A^\prime$, the image of $B$ as  $B^\prime$ and
the image of $C$ as $C^\prime$.
Draw the reflection of $\triangle A^{\prime}B^{\prime}C^\prime$ over the line $x = 2$. Label
the image of $A^\prime $ as $A^{\prime \prime}$, the image of $B^\prime$ as  $B^{\prime \prime}$ and
the image of $C^\prime$ as $C^{\prime \prime}$.
What single rigid transformation of the plane will map $\triangle ABC$ to
$\triangle A^{\prime \prime}B^{\prime \prime}C^{\prime \prime}$?  Explain.


aligns: no