Question

Read the following:Okay tm going to try to figure this out, so first, i would change A, B, and C using the first rule, which adds 4 to the x-coordinates and subtracts 6 from the y-coordinates. So A becomes (-4, -2), B becomes (-1, 2), and C becomes (1, -3). Then, i would apply the second rule to these new points, which adds 5 to the x-coordinates and subtracts 3 from the y-coordinates, giving me A" (1, -5), B" (4, -1), and C" (6, -6), which will be in Quadrant IV because both x and y are positive (vertex).

Solve the problem
Now, write your composition translation rule (add the two translation rules together)

Answer 1

To find the composition translation rule based on the two given translation rules, we can summarize the two rules as follows:

1. The first rule:
- Add 4 to the x-coordinates and subtract 6 from the y-coordinates.
- This can be expressed as:
\[
(x, y) \rightarrow (x + 4, y - 6)
\]

2. The second rule:
- Add 5 to the x-coordinates and subtract 3 from the y-coordinates.
- This can be expressed as:
\[
(x, y) \rightarrow (x + 5, y - 3)
\]

Now, to find the overall composition rule, we need to apply one translation after the other. We'll denote the original point as \( (x, y) \).

First, we apply the first rule:
\[
(x, y) \rightarrow (x + 4, y - 6)
\]

Next, we apply the second rule to the result from the first rule:
\[
(x + 4, y - 6) \rightarrow ((x + 4) + 5, (y - 6) - 3) \rightarrow (x + 9, y - 9)
\]

Thus, the overall composition translation rule, which combines both translations, is:
\[
(x, y) \rightarrow (x + 9, y - 9)
\]

In summary:
- The overall translation rule adds 9 to the x-coordinate and subtracts 9 from the y-coordinate.