Question

The triangle on the grid will be translated two units down.

On a coordinate plane, triangle A B C has points (2, 1), (0, negative 1), (2, negative 1).

Which shows the triangle when it is translated two units down?
On a coordinate plane, triangle A prime B prime C prime has points (0, negative 1), (0, negative 3), (2, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (0, 1), (negative 2, negative 1), (0, negative 1).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 3).
On a coordinate plane, triangle A prime B prime C prime has points (2, negative 1), (2, negative 3), (0, negative 1).

Answer 1

To translate the triangle down by two units, you need to subtract 2 from the y-coordinates of each vertex.

The original points of triangle ABC are:
- A(2, 1)
- B(0, -1)
- C(2, -1)

Now, we'll translate each point down by 2 units:

1. For point A(2, 1):
New A' = (2, 1 - 2) = (2, -1)

2. For point B(0, -1):
New B' = (0, -1 - 2) = (0, -3)

3. For point C(2, -1):
New C' = (2, -1 - 2) = (2, -3)

Thus, the new coordinates after translation are:
- A' = (2, -1)
- B' = (0, -3)
- C' = (2, -3)

Now, let's match these coordinates with the given options:

- **Option 1**: A'(0, -1), B'(0, -3), C'(2, -3) - **Does not match**
- **Option 2**: A'(0, 1), B'(-2, -1), C'(0, -1) - **Does not match**
- **Option 3**: A'(2, -1), B'(2, -3), C'(0, -3) - **Matches!**
- **Option 4**: A'(2, -1), B'(2, -3), C'(0, -1) - **Does not match**

Therefore, the correct option showing the triangle when it is translated two units down is **Option 3**: A'(2, -1), B'(2, -3), C'(0, -3).