https://file.aiquickdraw.com/mathbot/file/1725984784911tsmcohxe.jpg

The problem requires translating the parallelogram \( ABCD \) shown in the coordinate plane by 5 units to the left and 2 units down. We can solve this by adjusting the coordinates of each vertex of the parallelogram accordingly.

Let's start by identifying the coordinates of the vertices of the parallelogram \( ABCD \):
- \( A \) is at \( (0, 4) \),
- \( B \) is at \( (4, 4) \),
- \( C \) is at \( (6, 0) \),
- \( D \) is at \( (2, 0) \).

### Step 1: Translation Rule
The translation rule involves moving each point:
- 5 units to the left (subtract 5 from the \( x \)-coordinate),
- 2 units down (subtract 2 from the \( y \)-coordinate).

### Step 2: Apply the Translation
We apply the translation rule to each vertex:
1. \( A(0, 4) \) becomes \( A'(-5, 2) \),
2. \( B(4, 4) \) becomes \( B'(-1, 2) \),
3. \( C(6, 0) \) becomes \( C'(1, -2) \),
4. \( D(2, 0) \) becomes \( D'(-3, -2) \).

### Step 3: Plot the Translated Points
The new coordinates of the translated parallelogram are:
- \( A'(-5, 2) \),
- \( B'(-1, 2) \),
- \( C'(1, -2) \),
- \( D'(-3, -2) \).

Now you can graph the new parallelogram on the coordinate plane by plotting these points and connecting them in order \( A' \to B' \to C' \to D' \).

Would you like further details on how to graph this or any other questions?

### Relative Questions:
1. What is the general formula for translating points in the coordinate plane?
2. How would the parallelogram change if it were reflected instead of translated?
3. What is the effect of a translation on the area of a shape?
4. How can you verify the coordinates of a translated figure?
5. What are other types of transformations besides translation?

### Tip:
Always double-check translations by counting grid units to ensure accuracy.

Graph the image of the parallelogram after a translation of 5 units to the left and 2 units down.

Learn how to graph the image of a parallelogram ABCD after translating it 5 units left and 2 units down on the coordinate plane. Suitable for students in Grades 7-9, this problem involves applying the translation formula and plotting new coordinates.

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