To solve the problem of determining the translation that maps Figure $E$ onto Figure $F$, we need to calculate the horizontal and vertical shifts.

From the image:

• Figure $E$ is the lighter blue figure located around coordinates approximately $(-4, -3)$, $(-2, -5)$, and $(0, -4)$.
• Figure $F$ is the green figure located around coordinates approximately $(-8, -7)$, $(-6, -9)$, and $(-4, -8)$.

Steps:

1. Choose a point on Figure $E$ and map it to the corresponding point on Figure $F$. For example, take the top point of Figure $E$ located at $(-4, -3)$ and the corresponding top point of Figure $F$ at $(-8, -7)$.

2. Calculate the horizontal translation (shift along the x-axis): $x_{\text{shift}} = -8 - (-4) = -4$ So, the figure moves 4 units to the left.

3. Calculate the vertical translation (shift along the y-axis): $y_{\text{shift}} = -7 - (-3) = -4$ So, the figure moves 4 units down.

Translation:

• The translation to map Figure $E$ onto Figure $F$ is 4 units left and 4 units down.

You can enter this translation as:

• Horizontal: $-4$ units
• Vertical: $-4$ units

Would you like more details on any part of the process? Here are five related questions:

1. How can I confirm the translation by checking other points?
2. What if the figures had a rotation or reflection, how would that affect the solution?
3. How does translation differ from other transformations like dilation or rotation?
4. What is the general method to translate any geometric figure on a coordinate plane?
5. Can multiple translations be combined into a single step?

Tip: When working with translations, always use corresponding points on both figures to ensure accuracy in determining the shift.