Question

On the coordinate plane, point B (3,2) is translated to point B' (-3, 4). Which functions describe the two translation?

a. f (x) = x - 16 and g (y) = y + 12
b. f (x) = x + 6 and g (y) = y - 2
c. f (x) = x - 6 and g (y) = y + 2
d. f (x) = 6 - x and g (y) = 2 + y

Answer 1

To find the functions that describe the translation from point B (3, 2) to point B' (-3, 4), we need to determine the changes in the x and y coordinates.

1. **Change in x-coordinate**:
From 3 to -3, the change is:
\[
-3 - 3 = -6
\]
This indicates that the new x-coordinate is obtained by subtracting 6 from the original x-coordinate (3). Therefore, for the x-coordinate:
\[
f(x) = x - 6
\]

2. **Change in y-coordinate**:
From 2 to 4, the change is:
\[
4 - 2 = 2
\]
This means that the new y-coordinate is obtained by adding 2 to the original y-coordinate (2). Therefore, for the y-coordinate:
\[
g(y) = y + 2
\]

Combining these results, the translation functions are:
- \( f(x) = x - 6 \)
- \( g(y) = y + 2 \)

Now we can compare this with the options provided:

- a. \( f(x) = x - 16 \) and \( g(y) = y + 12 \)
- b. \( f(x) = x + 6 \) and \( g(y) = y - 2 \)
- c. \( f(x) = x - 6 \) and \( g(y) = y + 2 \)
- d. \( f(x) = 6 - x \) and \( g(y) = 2 + y \)

Based on our calculations, the correct answer is:

**c. \( f(x) = x - 6 \) and \( g(y) = y + 2 \)**