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

Option (1)

Step-by-step explanation:

Perpendicular bisector of the segment will pass through the midpoint of the segment joining two points (5, 7) and (-3, 3).

Midpoint of the segment will be,

(x, y) =

        =

        = (1, 5)

Slope of the line joining the given points =

     =

Let the slope of the line perpendicular to the segment joining the given points is .

By the property of perpendicular lines,

Since, equation of a line passing through (x', y') and slope 'm' is,

y - y' = m(x - x')

Therefore, equation of the line passing through (1, 5) and slope (-2) will be,

y - 5 = (-2)(x - 1)

y = -2x + 2 + 5

y = -2x + 7

2x + y = 7

Therefore, Option (1) will be the answer.

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step-by-step explanation: