Question

On this coordinate plane, point A (-2, 3) is translated into point A'(3, 5). Which functions give the two translations?

a. f (x) = x - 5 and g (y) = y - 2
b. f (x) = x + 6 and g (y) = y + 2
c. f (x) = x + 5 and g (y) = y + 2
d. f (x) = x + 2 and g (y) = y + 5

Answer 1

To find the translations from point A \((-2, 3)\) to point A' \( (3, 5) \), we can analyze the changes in the x-coordinate and y-coordinate separately.

1. **Change in x-coordinate:**
- Initial x = -2
- Final x = 3
- Change in x = 3 - (-2) = 3 + 2 = 5
- Therefore, we are translating the x-coordinate by adding 5: \( f(x) = x + 5 \)

2. **Change in y-coordinate:**
- Initial y = 3
- Final y = 5
- Change in y = 5 - 3 = 2
- Therefore, we are translating the y-coordinate by adding 2: \( g(y) = y + 2 \)

So the functions that give the translations are:
- \( f(x) = x + 5 \)
- \( g(y) = y + 2 \)

Now, let's look at the options:
- **a.** \( f(x) = x - 5 \) and \( g(y) = y - 2 \) (incorrect)
- **b.** \( f(x) = x + 6 \) and \( g(y) = y + 2 \) (incorrect for x)
- **c.** \( f(x) = x + 5 \) and \( g(y) = y + 2 \) (correct)
- **d.** \( f(x) = x + 2 \) and \( g(y) = y + 5 \) (incorrect)

The correct answer is **c. \( f(x) = x + 5 \) and \( g(y) = y + 2 \)**.