Preimage polygon VWYZ and image polygon V′W′Y′Z′ are shown on a coordinate plane.

Question

polygon VWYZ with vertices at V 5 comma 8, W 5 comma 2, Y 11 comma 2, and Z 11 comma 8 and polygon V prime W prime Y prime Z prime with vertices at V prime 5 comma negative 8, W prime 5 comma negative 2, Y prime 11 comma negative 2, and Z prime 11 comma negative 8

What transformation takes polygon VWYZ to polygon V′W′Y′Z′?
Vertical translation
90° clockwise rotation
Reflection across the y-axis
Reflection across the x-axis

Answer 1

To determine the transformation that takes polygon VWYZ to polygon V′W′Y′Z′, we need to analyze the coordinates of the vertices.

The vertices of polygon VWYZ:

• \( V(5, 8) \)
• \( W(5, 2) \)
• \( Y(11, 2) \)
• \( Z(11, 8) \)

The vertices of polygon V′W′Y′Z′:

• \( V′(5, -8) \)
• \( W′(5, -2) \)
• \( Y′(11, -2) \)
• \( Z′(11, -8) \)

We notice that the y-coordinates of the vertices of polygon V′W′Y′Z′ are the negations of the y-coordinates of polygon VWYZ.

This indicates that each point is reflected across the x-axis. The transformation that takes polygon VWYZ to polygon V′W′Y′Z′ is thus:

Reflection across the x-axis.