Which segment is the image of Line segment A B reflected across the line y = negative 2?

On a coordinate plane, segment A B goes from (2, negative 7) to (8, negative 3), segment J K goes from (2, 7) to (8, 3), segment G H goes from (2, 3) to (8, negative 1), segment F A goes from (negative 4, negative 3) to (2, negative 7), and C D goes from (negative 8, negative 3) to (negative 2, negative 7).
Line segment A F
Line segment D C
Line segment G H
Line segment J K

The image of Line segment AB is the Line segment GH

Step-by-step explanation:

we have

segment AB

A(2,-7) and B(8,-3)

The segment AB is reflected across the line  y=-2

The line is parallel to the x-axis

Remember that

If we reflect about a line that is parallel to the x-axis, then the x-coordinate of the point (that is reflected) will remain the same,

thus

the image of A (2,-7) has x-coordinate 2 and thus the point is of the form (2,a)

and

the image of B(8,-3) has x-coordinate 8 and thus the point is of the form (8,b)

Determine the y-coordinate a

The point A (2,-7) is 5 units from the line y=-2 (because the difference between y=-7 and y=-2 is 5)

The reflected point has to be the same distance from the line y=-2 than the original point and is not the original point (because the original point does not lie on the line), thus the distance from (2,a) to y=-2 has to be 5

a=-2+5=3

a=-2-5=-7

Since a=-7 leads to the original point, a=3 corresponds with the reflected point and thus the coordinates of the reflected point are (2,a)=(2,3).

Determine the y-coordinate b

The point B (8,-3) is 1 unit from the line y=-2 (because the difference between y=-3 and y=-2 is 1)

The reflected point has to be the same distance from the line y=-2 than the original point and is not the original point (because the original point does not lie on the line), thus the distance from (8,b) to y=-2 has to be 1

b=-2+1=-1

b=-2-1=-3

Since b=-3 leads to the original point, b=-1 corresponds with the reflected point and thus the coordinates of the reflected point are (8,b)=(8,-1).

so

The image of  line segment AB are the points (2,3) and (8,-1)

we have that

point (2,3) is the point G

point (8,-1) is the point H

therefore

The image of Line segment AB is the Line segment GH

8(-10x+3.5y-7)

8×-10x + 8×3.5y + 8×-7

-80x + 28y - 56

therefore

-80x+28y-56 is the correct answer