Question

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

Answer 1

Option (1)

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) =
`((x_1+x_2)/(2),(y_1+y_2)/(2))`

=
`((5-3)/(2),(7+3)/(2))`

= (1, 5)

Slope of the line joining the given points
`m_1` =
`(y_2-y_1)/(x_2-x_1)`

`m_1=(7-3)/(5+3)`

=
`(1)/(2)`

Let the slope of the line perpendicular to the segment joining the given points is
`m_2`.

By the property of perpendicular lines,

`m_1* m_2=-1`

`(1)/(2)* m_2=-1`

`m_2=-2`

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.