To solve this problem, we need to apply the translation to each of the vertices of the quadrilateral.

The translation is:

• Up 2 units (this means adding 2 to the y-coordinate).
• Left 1 unit (this means subtracting 1 from the x-coordinate).

Given vertices:

• A(-4, -2)
• B(-5, 3)
• C(6, 2)
• D(9, -1)

Translation Steps:

For each vertex, we apply the translation as follows:

1. New x-coordinate = original x-coordinate - 1
2. New y-coordinate = original y-coordinate + 2

Now, let’s calculate the new coordinates:

1. A':

   • Original: A(-4, -2)
   • New x = -4 - 1 = -5
   • New y = -2 + 2 = 0
   • A'(-5, 0)

2. B':

   • Original: B(-5, 3)
   • New x = -5 - 1 = -6
   • New y = 3 + 2 = 5
   • B'(-6, 5)

3. C':

   • Original: C(6, 2)
   • New x = 6 - 1 = 5
   • New y = 2 + 2 = 4
   • C'(5, 4)

4. D':

   • Original: D(9, -1)
   • New x = 9 - 1 = 8
   • New y = -1 + 2 = 1
   • D'(8, 1)

Final Translated Coordinates:

• A'(-5, 0)
• B'(-6, 5)
• C'(5, 4)
• D'(8, 1)

Let me know if you want more details on the translation process or have any questions!

Here are 5 related questions you might consider:

1. How do translations differ from rotations or reflections in geometry?
2. What is the effect of translating a point by $(a, b)$?
3. How do you find the area of a quadrilateral given its vertices?
4. How would the coordinates change if the translation was down instead of up?
5. Can you describe a translation using vector notation?

Tip:

Always check if the translation is positive (up/right) or negative (down/left) to adjust the coordinates accordingly.