Final answer:
To find the equation of the perpendicular bisector of the segment with endpoints G(2,0) and H(8,6), find the midpoint, calculate the slope, and determine the negative reciprocal. Substitute the values into the slope-intercept form to find the equation of the perpendicular bisector: y = -x + 8.
Step-by-step explanation:
To find the equation of the perpendicular bisector of the segment with endpoints G(2,0) and H(8,6) in slope-intercept form, we need to find the midpoint of the segment and the slope of the perpendicular bisector.
The midpoint of the segment is given by the formula:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
Using the endpoints G(2,0) and H(8,6), we find that the midpoint is M(5,3).
The slope of the original segment is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the endpoints G(2,0) and H(8,6), we find that the slope of the original segment is 1.
The perpendicular bisector of a line has a slope that is the negative reciprocal of the original line. Therefore, the slope of the perpendicular bisector is -1.
Using the slope-intercept form of a line, y = mx + b, and the point M(5,3), we can substitute the values of the slope and the coordinates of the midpoint to find the equation of the perpendicular bisector:
y = -1x + b
3 = -1(5) + b
b = 8
Therefore, the equation of the perpendicular bisector is y = -x + 8.