Question

On a coordinate plane, 5 trapezoids are shown. Trapezoid L M N P is in quadrant 2 and has points (negative 5, 1), (negative 5, 4), (negative 3, 4), and (negative 3, 2). Trapezoid A is reflected across the x-axis. Trapezoid B is shifted 3 units to the right and 2 units down. Trapezoid C is reflected across the y-axis. Trapezoid D is in quadrant 4 and is rotated.
Trapezoid LMNP was reflected using the rule
ry–axis(x, y) → (–x, y). Which figure represents the image of the reflection?

figure

Answer 1

To find the image of trapezoid L M N P after reflecting it across the y-axis, you need to apply the reflection rule \( r_{y-axis}(x, y) \rightarrow (-x, y) \) to each vertex of trapezoid L M N P.

The original vertices of trapezoid L M N P are:
- \( L(-5, 1) \)
- \( M(-5, 4) \)
- \( N(-3, 4) \)
- \( P(-3, 2) \)

Now, we will apply the reflection rule:

1. For point L:
\[
(-5, 1) \rightarrow (5, 1)
\]

2. For point M:
\[
(-5, 4) \rightarrow (5, 4)
\]

3. For point N:
\[
(-3, 4) \rightarrow (3, 4)
\]

4. For point P:
\[
(-3, 2) \rightarrow (3, 2)
\]

So, the coordinates of the reflected trapezoid are:
- \( L'(5, 1) \)
- \( M'(5, 4) \)
- \( N'(3, 4) \)
- \( P'(3, 2) \)

To identify the correct figure representing the image of this reflection, you would need to find corresponding points \( (5, 1), (5, 4), (3, 4), (3, 2) \) in the provided figures.

Look for a trapezoid with vertices matching these coordinates to determine which figure represents the image of the reflection of trapezoid L M N P across the y-axis.