Question

What image is the translation of ΔABC given by the translation rule (x, y) → (x + 2, y – 2)?


graph

Answer 1

I cannot directly produce a graph for you, but I can explain what the translated image of ΔABC would look like under the given translation rule (x, y) → (x + 2, y – 2).

The translation rule (x, y) → (x + 2, y – 2) means that every point on triangle ΔABC will be moved 2 units right and 2 units down. Here's how you can visualize the translation:

1. Take every vertex (corner) of ΔABC and note its coordinates.
2. Apply the translation rule to each vertex. For example, if one vertex of ΔABC is at (3, 5), applying the translation rule will move this vertex to (3 + 2, 5 - 2), which is (5, 3).
3. Do this for the other two vertices.
4. Once you have the new coordinates for the three vertices, plot them on the graph.
5. Connect the new vertices with lines to form the new triangle ΔA'B'C'.

This new triangle ΔA'B'C' will have the same shape and size as ΔABC; it will just be located in a different position on the graph—specifically, 2 units to the right and 2 units down from the original position of ΔABC.

If ΔABC had vertices at points (a, b), (c, d), and (e, f), then the translated vertices of ΔA'B'C' would be at points (a+2, b-2), (c+2, d-2), and (e+2, f-2).