Answer: The equation for the perpendicular bisector of line segment xy is .
Explanation:
It is given that the line segment xy has endpoints x(5,7) and y(-3,3).
The bisector divides the line segment xy in two equal parts, so the bisector must be passing through the midpoint of xy.
Midpoint of two points (x_1,y_1) and (x_2,y_2) is calculated as,
Midpoint of xy is,
So, the perpendicular bisector must be passing through the point (1,5).
The slope of line passing through the point (x_1,y_1) and (x_2,y_2) is calculated as,
Slope of line segment is . Therefore the slope of perpendicular bisector is -2 because the the product of slopes of two perpendicular lines is always -1.
The line passing through the point (x_1,y_1) with slope m is defined as,
Bisector passing through the point (1,5) with slope 2.
Therefore, the equation for the perpendicular bisector of line segment xy is .