Question

which of the following best describes the transformation from rectangle pqrs to rectangle pqrs?
grid with rectangles pqrs (white) and pqrs (blue) shown

• reflection across y=0
• translate 11 units left
• translation 11 units right
• reflection across x=0

Explanation:

Step1: Analyze Reflection vs Translation

Check if it's a reflection (mirror image) or translation (slide). The rectangles are on opposite sides of the y - axis (x = 0 is y - axis? Wait, no, x = 0 is y - axis, y = 0 is x - axis. Wait, the original rectangle PQRS (let's say the white one) and the blue one. Wait, the labels: P, Q, R, S for white; P', Q', R', S' for blue? Wait, looking at the grid, the white rectangle is on the left of the y - axis, blue on the right. A reflection across x = 0 (y - axis) would flip it over the y - axis. Let's check translation: moving 11 units right? Let's count the distance between corresponding points. But reflection across x = 0 (y - axis) would make the image a mirror over y - axis. The other options: reflection across y = 0 (x - axis) would flip vertically, but the rectangles are horizontal. Translation left/right: but the shape is mirrored, not just moved. So the correct transformation is reflection across x = 0.

Step2: Evaluate Each Option

• Reflection across y = 0: Flips over x - axis, but the rectangles are horizontal, same y - level. Eliminate.
• Translate 11 units left: Would move the blue rectangle to the left, but it's on the right. Eliminate.
• Translate 11 units right: Would move the white rectangle to the right, but the blue is a mirror, not a translation. Eliminate.
• Reflection across x = 0: Flips over y - axis, which matches the position (left and right of y - axis). Correct.

Answer:

Reflection across \( x = 0 \) (the option corresponding to "Reflection across \( x = 0 \)")