To write the translation rule for $\overline{XY} \rightarrow \overline{X'Y'}$, let's first determine the coordinates of points $X$, $Y$, $X'$, and $Y'$.

• $X$ is at $(-2, -1)$
• $Y$ is at $(-1, -3)$
• $X'$ is at $(8, 4)$
• $Y'$ is at $(9, 2)$

Now, let's calculate the translation by finding the differences in the coordinates between the original and translated points:

1. Translation from $X$ to $X'$: $\Delta x = 8 - (-2) = 10, \quad \Delta y = 4 - (-1) = 5$

2. Translation from $Y$ to $Y'$: $\Delta x = 9 - (-1) = 10, \quad \Delta y = 2 - (-3) = 5$

Both points are translated by the same amount, so the translation rule is: $(x, y) \rightarrow (x + 10, y + 5)$

This is the translation rule for the transformation.

Would you like more details, or do you have any questions?

Related Questions:

1. What is a general definition of translation in geometry?
2. How do you find the translation rule for any two given points?
3. Can translations change the size or shape of a figure?
4. How do reflections differ from translations?
5. What other transformations can you apply to a figure in the coordinate plane?

Tip:

Always make sure to verify that both points in a segment undergo the same translation to confirm the rule!