Line segment XY has endpoints X(5, 7) and Y(– 3, 3). Find the equation for the perpendicular bisector of line segment XY.

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 .