Question

Which of the following rules would translate A ABC 5 units left and 3 units up?
Option #1: (x, y) → (х - 5, y + 3) Option #2: (x, y) → (5x, 3y)
Option #3: (x, y) → (х + 3, y - 5)
(1 point)

Answer 1

To translate a point \( A \) with coordinates \( (x, y) \) by 5 units left and 3 units up, you would subtract 5 from the x-coordinate and add 3 to the y-coordinate.

The translation can be represented as:

\[
(x, y) \rightarrow (x - 5, y + 3)
\]

Now let's examine the options:

- **Option #1:** \( (x, y) \rightarrow (x - 5, y + 3) \) — This is correct, as it matches the translation specified.
- **Option #2:** \( (x, y) \rightarrow (5x, 3y) \) — This is incorrect, as it involves scaling rather than translating.
- **Option #3:** \( (x, y) \rightarrow (x + 3, y - 5) \) — This is incorrect, as it moves the point in the opposite direction.

Based on this analysis, the correct option for translating \( A \) 5 units left and 3 units up is **Option #1: (x, y) → (x - 5, y + 3)**.