Question

Right triangle LMN has vertices L(7, –3), M(7, –8), and
N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Which rule was used to translate the image?

(x, y) → (x + 6, y – 5)
(x, y) → (x – 6, y + 5)
(x, y) → (x + 8, y – 11)
(x, y) → (x – 8, y + 11)

Answer 1

To determine which translation rule was used, we can compare the original coordinates of point L(7, -3) with the coordinates of the translated point L'(-1, 8).

Let's find the changes in the x and y coordinates:

1. Change in x-coordinates:
\[
-1 - 7 = -8
\]

2. Change in y-coordinates:
\[
8 - (-3) = 8 + 3 = 11
\]

Therefore, the translation changes the points as follows:
- The x-coordinate decreases by 8.
- The y-coordinate increases by 11.

This means the translation rule can be expressed as:
\[
(x, y) \rightarrow (x - 8, y + 11)
\]

Thus, the correct translation rule that was used is \((x, y) \rightarrow (x - 8, y + 11)\).