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A line segment has endpoints at (–4, –6) and (–6, 4). Which reflection will produce an image with endpoints at (4, –6) and (6, 4)?
a reflection of the line segment across the x-axis
a reflection of the line segment across the y-axis
a reflection of the line segment across the line y = x
a reflection of the line segment across the line y = –x
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a reflection of the line segment across the y-axis

Explanation:

The transformations of the end points are:

       Preimage         Image

(–4, –6)     →    (4, –6) (–6, 4)       →    (–6, 4)

The means that, for every end point, the x-coordinate changes the sign and the y-coordinate remains unchanged.

That rule is:

(x, y) → (- x, y): this is a reflection across the y-axis.

Keeping the y-coordinate and changing the sign of the x-coordinate is a reflection across the y -axis. It is like a mirror image, where the mirror is placed along the y-axis. The figure keeps the same distance from the y-axis (the mirror) but changes sides, which is represented by the change of x to - x,  while the altitude (the y-coordinate) keeps unchanged.

Mexico has a host of environmental problems, including significant chemicalpollution  from factory discharges and waste dumping, but the main threat to itsbiodiversity  probably stems from  deforestation  and other natural habitat losses. forest habitat is lost for a number of reasons

Forms from the water cycle