Question

Use the graph to answer the question.

graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3

Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 90° counterclockwise.

A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)
A′(0, 0), B′(−2, −5), C′(−5, 5), D′(−3, 0)
A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0)
A′(0, 0), B′(−5, −2), C′(−5, −5), D′(0, 3)

Answer 1

To determine the coordinates of polygon A′B′C′D′ when polygon ABCD is rotated 90° counterclockwise, we can apply the rotation transformation rule. The transformation for a point (x, y) rotated 90° counterclockwise around the origin is given by the formula:

\[
(x, y) \rightarrow (-y, x)
\]

We can apply this rule to each vertex of polygon ABCD:

1. **Vertex A (0, 0)**:
\[
(0, 0) \rightarrow (0, 0)
\]

2. **Vertex B (5, 2)**:
\[
(5, 2) \rightarrow (-2, 5)
\]

3. **Vertex C (5, -5)**:
\[
(5, -5) \rightarrow (5, -5)
\]

4. **Vertex D (0, -3)**:
\[
(0, -3) \rightarrow (3, 0)
\]

Thus, the coordinates of A′B′C′D′ after the rotation would be:

- A′(0, 0)
- B′(−2, 5)
- C′(−5, 5)
- D′(3, 0)

Now, match these with the options provided:

1. **A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)** - Does not match C.

2. **A′(0, 0), B′(−2, −5), C′(−5, 5), D′(−3, 0)** - Does not match B.

3. **A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0)** - Does not match C.

4. **A′(0, 0), B′(−5, −2), C′(−5, −5), D′(0, 3)** - Does not match D.

It seems that there's an error with the given options, as none of them matches the transformed coordinates. Please double-check the options or the transformation specifics.