2. Reflections
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Reflected points are the same distance from opposite sides of the line of reflection.
Graph:
Vertices: A'( 5,- 1), B'(1,- 2), C'(6,- 2)
Let's start by plotting the given points and connecting them to draw our triangle.
We want to reflect this figure over the x-axis. To do so, we need to plot each vertex of the image A'B'C' the same distance from the line of reflection as its corresponding vertex on the preimage ABC. Because our line of reflection is the x-axis, this will change the sign of the y-coordinates of the points, but the x-coordinates will remain unchanged.
| Preimage ABC | Image A'B'C' | ||
|---|---|---|---|
| Vertex | Distance From the x-axis | Vertex | Distance From the x-axis |
| A(5,1) | 1 unit above the x-axis | A'(5,- 1) | 1 unit below the x-axis |
| B(1,2) | 2 units above the x-axis | B'(1,- 2) | 2 units below the x-axis |
| C(6,2) | 2 units above the x-axis | C'(6,- 2) | 2 units below the x-axis |