Answer:
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)
<u><em>Determine the y-coordinate a</em></u>
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).
<u><em>Determine the y-coordinate b</em></u>
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
