Final answer:
To find the equation for the perpendicular bisector of the line segment with endpoints A(4, 8) and B(10, 2), we need to find the midpoint of the line segment and then determine the negative reciprocal of the slope of the line segment. The equation of the perpendicular bisector is y = x - 2.
Step-by-step explanation:
To find the equation for the perpendicular bisector of the line segment with endpoints A(4, 8) and B(10, 2), we need to find the midpoint of the line segment and then determine the negative reciprocal of the slope of the line segment.
The midpoint of the line segment is found by averaging the x-coordinates and the y-coordinates of the endpoints.
In this case, the midpoint is (7, 5).
The negative reciprocal of the slope of the line segment can be found by taking the negative reciprocal of the slope, which is given by the formula (y2 - y1) / (x2 - x1).
In this case, the slope of the line segment is -1.
Therefore, the equation of the perpendicular bisector will have a slope of 1 and pass through the midpoint (7, 5).
Using the point-slope form of a linear equation, the equation of the perpendicular bisector is y = x - 2.