Question

Rectangle RSTU
is reflected around the x
-axis and then around the y
-axis to create rectangle R′S′T′U′
. Which statement is true?(1 point)

If vertex R
has negative x
- and y
-coordinates, vertex R′
will also have negative x
- and y
-coordinates.

If vertex R
has negative x
- and y
-coordinates, vertex R′
will have a positive x
-coordinate and a negative y
-coordinate.

If vertex R
has negative x
- and y
-coordinates, vertex R′
will have positive x
- and y
-coordinates.

If vertex R
has negative x
- and y
-coordinates, vertex R′
will have a negative x
-coordinate and a positive y
-coordinate.
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Answer 1

Correct answer: "If vertex R has negative x- and y-coordinates, vertex R′ will have positive x- and y-coordinates."

Reason: Reflection across the x-axis changes (x,y) to (x,−y) (y sign flips). Then reflecting across the y-axis changes (x,−y) to (−x,−y) (x sign flips). Starting with (−x,−y) (both negative) gives (positive, positive).