Question

Point A(7, 3) is translated to A prime (16, negative 9). Which rule describes the translation?
(x, y) right-arrow (x minus 9, y minus 12)
(x, y) right-arrow (x minus 9, y + 12)
(x, y) right-arrow (x + 9, y + 12)
(x, y) right-arrow (x + 9, y minus 12)

Answer 1

To determine the rule for the translation from point A(7, 3) to A' (16, -9), we need to find out how the x-coordinates and y-coordinates change.

1. **Change in x-coordinate**:
- From 7 to 16:
\( 16 - 7 = 9 \)
Thus, the x-coordinate increases by 9.

2. **Change in y-coordinate**:
- From 3 to -9:
\( -9 - 3 = -12 \)
Thus, the y-coordinate decreases by 12.

This can be summarized as:
- The x-coordinate is increased by 9.
- The y-coordinate is decreased by 12.

Therefore, the translation rule can be expressed as:
\[
(x, y) \rightarrow (x + 9, y - 12)
\]

Thus, the correct answer is:
(x, y) right-arrow (x + 9, y - 12).