Question

On a coordinate plane, 2 trapezoids are shown. The first trapezoid has points A (negative 1, 0), B (0, 2), C (3, 2), and D (4, 0). The second trapezoid has points A prime (negative 1, 0), B prime (0, negative 2), C prime (3, negative 2), and D prime (4, 0).
What is the rule for the reflection?

ry-axis(x, y) → (–x, y)
ry-axis(x, y) → (x, –y)
rx-axis(x, y) → (–x, y)
rx-axis(x, y) → (x, –y)

Answer 1

To determine the rule for the reflection from the first trapezoid to the second trapezoid, let's analyze the coordinates of the points provided:

For the first trapezoid:
- Point A: \((-1, 0)\)
- Point B: \((0, 2)\)
- Point C: \((3, 2)\)
- Point D: \((4, 0)\)

For the second trapezoid:
- Point A prime: \((-1, 0)\)
- Point B prime: \((0, -2)\)
- Point C prime: \((3, -2)\)
- Point D prime: \((4, 0)\)

Looking at the coordinates of the trapezoids:
- The points A and A prime are the same: \((-1, 0)\) remains unchanged.
- The \(y\)-coordinates of points B and C from the first trapezoid change from positive to negative in the second trapezoid.

When reflecting over the x-axis, the transformation rule is:
\[
(x, y) \rightarrow (x, -y)
\]

This means the x-coordinates remain the same, while the y-coordinates change sign.

Thus, the reflection reflecting points B and C from \((0, 2)\) to \((0, -2)\) and from \((3, 2)\) to \((3, -2)\) confirms this.

Therefore, the rule for the reflection from the first trapezoid to the second trapezoid is:
\[
\text{rx-axis}(x, y) \rightarrow (x, -y)
\]