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# What are the steps for finding the perpendicular bisect of a line segment?

Updated: 12/3/2022

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Q: What are the steps for finding the perpendicular bisect of a line segment?
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To solve this, four steps are needed:Find the midpoint of the line segment (X, Y) which is a point on the perpendicular bisectorFind the slope m for the line segment: m = change_in_y/change_in_xFind the slope m' of the perpendicular line; the slopes of the lines are related by mm' = -1 &rarr; m' = -1/mFind the equation of the perpendicular bisector using the slope-point equation for a line passing through point (X, Y) with slope m': y - Y = m'(x - X)Have a go before reading the solution below.--------------------------------------------------------------------The midpoint of (7, 3) and (-6, 1) is at ((7 + -6)/2, (3 + 1)/2) = (1/2, 2)The slope of the line segment is: m = change_in_y/change_in_x = (1 - 3)/(-6 - 7) = -2/-13 = 2/13The slope of the perpendicular bisector is m' = -1/m = -1/(2/13) = -13/2The equation of the perpendicular bisector passing through point (X, Y) = (1/2, 2) with slope m' = -13/2 is given by:y - Y = m'(x - Y)&rarr; y - 2 = -13/2(x - 1/2)&rarr; 4y - 8 = -26x + 13&rarr; 4y + 26x = 21

### How do you construct 90 degree angle with compass with construction steps?

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