Question

On a coordinate plane, triangle A B C is shifted 4 units up and 3 units to the left to form triangle A prime B prime C prime.
Use the figure to identify the correct rule for the translation.
(x, y) Right-arrow (x – 3, y + 4)
(x, y) Right-arrow (x + 3, y – 4)
(x, y) Right-arrow (x – 4, y + 3)
(x, y) Right-arrow (x + 4, y – 3)

Answer 1

To determine the correct translation rule for moving triangle ABC to triangle A'B'C', we need to analyze the shifts in the x and y coordinates.

1. **Shifting 3 units to the left** decreases the x-coordinate by 3. Therefore, the x-coordinate will change as follows:
\[
x' = x - 3
\]

2. **Shifting 4 units up** increases the y-coordinate by 4. Hence, the y-coordinate will change as follows:
\[
y' = y + 4
\]

Combining these transformations gives us the translation rule:
\[
(x, y) \rightarrow (x - 3, y + 4)
\]

Therefore, the correct rule for the translation is:
\[
(x, y) \rightarrow (x - 3, y + 4)
\]