To find the glide reflection image of a blue triangle when you have a specific translation and a line of reflection, there are a few steps to follow. Here, we will break it down into manageable parts.
Step 1: Understand the Components
A glide reflection is a combination of two transformations: a translation followed by a reflection across a line. In this case, our translation vector is (7, 0) and the line of reflection is given by the equation x = 1.
Step 2: Translate the Triangle
Start by translating the coordinates of each vertex of the blue triangle using the translation vector. For example, if the vertices of the triangle are A(x1, y1), B(x2, y2), and C(x3, y3), after applying the translation, the new coordinates will be:
- A’ = (x1 + 7, y1)
- B’ = (x2 + 7, y2)
- C’ = (x3 + 7, y3)
This shifts the triangle horizontally to the right by 7 units.
Step 3: Reflect the Translated Triangle
The next step is to reflect each of the translated points A’, B’, and C’ across the line of reflection x = 1. To find the reflected points, use the formula:
If a point P(x, y) is reflected over the line x = k, the new point P'(x’, y) will be:
x’ = 2k – x
In our case, k = 1. Thus for each reflected point:
- A” = (2*1 – (x1 + 7), y1) = (2 – (x1 + 7), y1) = (-x1 – 5, y1)
- B” = (2 – (x2 + 7), y2) = (-x2 – 5, y2)
- C” = (2 – (x3 + 7), y3) = (-x3 – 5, y3)
Step 4: The Final Glide Reflection Image
The final coordinates of the glide reflection image of the blue triangle will be:
- A” = (-x1 – 5, y1)
- B” = (-x2 – 5, y2)
- C” = (-x3 – 5, y3)
These points represent the vertices of the triangle after undergoing the glide reflection transformation. By following these steps, you can effectively find the glide reflection image for any geometric figure.