Find the equation in point-slope form of the line that is the perpendicular bisector of the segment betweeen (16,-4) and (-2,-76)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to write the point slope form of equation of the line that is the perpendicular bisector of the segment between (16,-4) and (-2,-76), hence, you need to find the coordinates of the midpoint of segment and you need to find the slope of the line.

You need to use the equations that relates the coordinates of midpoint and the coordinates of endpoints of segment, such that:

`x = (x_1 + x_2)/2 => x = (16 - 2)/2 => x = 7`

`y = (y_1 + y_2)/2 => y = (-4 - 76)/2 = -40`

Hence, evaluating the coordinates of the midpoint yields (7,-40).

You need to use the equation that relates the slopes of two perpendicular lines, such that:

`m_1 *m_2 = -1 `

Considering `m_1` the slope of the segment, yields:

`m_1 = (y_2 - y_1)/(x_2 - x_1) => m_1 = (-76 + 4)/(-2 + 4)`

`m_1 = (-72)/2 => m_1 = -36`

`m_2 = -1/(m_1) => m_2 = 1/36`

Hence, evaluating the point slope form of equation of perpendicular bisector of the segment between (16,-4) and (-2,-76) yields:

`y - (-40) = m_2(x - 7) => y + 40 = 1/36(x - 7)`

`y = x/36 - 7/36 - 40`

Hence, evaluating the point slope form of equation of perpendicular bisector of the segment between (16,-4) and (-2,-76) yields `y = x/36 - 7/36 - 40.`

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