Question

What kind of translation has been done to quadrilateral ABCD?
Quadrilateral ABCD has been translated ___ units to the right and ___ units down.

Quadrilateral ABCD:
Point A: (2, 2)
Point B: (6, 4)
Point C: (10, 4)
Point D: (6, 2)

Quadrilateral EFGH:
Point E: (11, -1)
Point F: (15, -1)
Point G: (19, 1)
Point H: (15, 1)

Answer 1

To determine the translation from quadrilateral ABCD to quadrilateral EFGH, we need to compare the coordinates of corresponding points before and after the translation.

**Coordinates of quadrilateral ABCD:**
- Point A: (2, 2)
- Point B: (6, 4)
- Point C: (10, 4)
- Point D: (6, 2)

**Coordinates of quadrilateral EFGH:**
- Point E: (11, -1)
- Point F: (15, -1)
- Point G: (19, 1)
- Point H: (15, 1)

Next, we'll find the translation for point A to point E as it helps to understand the translation for other points as well:

1. For Point A to Point E:
- Change in x: 11 - 2 = **9 units to the right**
- Change in y: -1 - 2 = **-3 units down**

Now, let's check if the same translation applies to the other points:

2. Point B to Point F:
- Change in x: 15 - 6 = 9 units to the right
- Change in y: -1 - 4 = -5 units down (not consistent)

3. Point C to Point G:
- Change in x: 19 - 10 = 9 units to the right
- Change in y: 1 - 4 = -3 units down (consistent)

4. Point D to Point H:
- Change in x: 15 - 6 = 9 units to the right
- Change in y: 1 - 2 = -1 unit down (not consistent)

From the calculations:
- Point A, C have consistent changes of 9 units to the right and -3 units down.
- Point B has a different downward change.
- Point D also has a different downward change.

Since the movement from A to E and C to G can be seen as a consistent translation of 9 units to the right and 2 units down (the average vertical translation between consistent pairs).

Thus, combining the results:

Quadrilateral ABCD has been translated **9 units to the right and approximately 3 units down on average** with some inconsistencies on points B and D.

So, the translation can be summarized as:

**Quadrilateral ABCD has been translated 9 units to the right and approximately 3 units down.**