Question

A triangle has vertices at L(2, 2), M(4, 4), and N(1, 6). The triangle is transformed according to the rule R0, 180°.

Which statements are true regarding the transformation? Select three options.

The rule for the transformation is (x, y) → (–x, –y).
The coordinates of L' are (–2,–2).
The coordinates of M' are (–4,4).
The coordinates of N' are (6,–1).
The coordinates of N' are (–1,–6).

Answer 1

To determine the coordinates of the vertices of the triangle after the transformation R0, 180°, we need to understand what this transformation entails. The transformation R0, 180° means rotating the triangle 180 degrees around the origin (0, 0).

The transformation rule for rotating a point (x, y) around the origin by 180 degrees is given by the following transformation:

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

Let's apply this transformation to each vertex of the triangle:

1. **Vertex L(2, 2)**:
\[
L' = (2, 2) \rightarrow (-2, -2)
\]

2. **Vertex M(4, 4)**:
\[
M' = (4, 4) \rightarrow (-4, -4)
\]

3. **Vertex N(1, 6)**:
\[
N' = (1, 6) \rightarrow (-1, -6)
\]

Now, we evaluate the given options:

1. **The rule for the transformation is (x, y) → (–x, –y).**
- **True**: This is the correct rule for a 180-degree rotation around the origin.

2. **The coordinates of L' are (–2, –2).**
- **True**: As calculated, L' is indeed (-2, -2).

3. **The coordinates of M' are (–4, 4).**
- **False**: The coordinates of M' are (-4, -4), not (-4, 4).

4. **The coordinates of N' are (6, –1).**
- **False**: The coordinates of N' are (-1, -6), not (6, -1).

5. **The coordinates of N' are (–1, –6).**
- **True**: As calculated, N' is indeed (-1, -6).

Thus, the three true statements regarding the transformation are:

1. The rule for the transformation is (x, y) → (–x, –y).
2. The coordinates of L' are (–2, –2).
3. The coordinates of N' are (–1, –6).