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

We want to see which reflection we need to use to transform the given segment into the desired one.

The correct answer is:

"a reflection of the line segment across the y-axis"

First, we want to change the segment with endpoints at (-4, -6) and (-6, 4) to a segment with endpoints (4, -6) and (6, 4).

Note that the only thing that changes is the x-value of the endpoints, so we need to apply a reflection that only changes the x-value.

That reflection is a reflection across the y-axis.

For a general point (x, y), a reflection across the y-axis transforms the point to (-x, y).

Then the correct option is:

"a reflection of the line segment across the y-axis"

If you want to learn more, you can read:

link

reflection in the y- axis

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Note the x- coordinate is opposite in sign and the y- coordinate remains unchanged.

Thus

(- 4, - 6 ) → (4, - 6 )

(- 6, 4 ) → (6, 4 )

The endpoints have been reflected in the y- axis