Q: What is the perpendicular bisector equation passing through the line segment of 7 7 and 3 5 giving brief details?

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First find the midpoint of (-2, 5) and (-8, -3) which is (-5, 1) Then find the slope of (-2, 5) and (-8, -3) which is 4/3 Slope of the perpendicular bisector is the negative reciprocal of 4/3 which is -3/4 Now form an equation of the straight line with a slope of -3/4 passing through the point (-5, 1) using the formula y-y1 = m(x-x1) The equation works out as: 3x+4y+11 = 0

Known equation: 5x-2y = 3 or y = 5/2x -3/2 Slope of known equation: 5/2 Slope of perpendicular equation: -2/5 Perpendicular equation: y- -4 = -2/5(x-3) => 5y =-2x-14 Perpendicular equation in its general form: 2x+5y+14 = 0

There is no name for it except "A line perpendicular to a line segment and passing through its midpoint".

7x-y-28 = 0

If: 4x+3y-5 = 0 then y = -4/3x+5/3 Slope is -4/3 and so the perpendicular slope is 3/4 Perpendicular equation: y--3 = 3/4(x--2) => 4y--12 = 3x+6 => 4y = 3x-6

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Points: (3,-4) and (-1, -2) Midpoint: (1,-3) Slope: -1/2 Perpendicular slope: 2 Perpendicular bisector equation in slope intercept form: y = 2x-5

First find the midpoint of (-2, 5) and (-8, -3) which is (-5, 1) Then find the slope of (-2, 5) and (-8, -3) which is 4/3 Slope of the perpendicular bisector is the negative reciprocal of 4/3 which is -3/4 Now form an equation of the straight line with a slope of -3/4 passing through the point (-5, 1) using the formula y-y1 = m(x-x1) The equation works out as: 3x+4y+11 = 0

8

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 → 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)→ y - 2 = -13/2(x - 1/2)→ 4y - 8 = -26x + 13→ 4y + 26x = 21

Known equation: 5x -2y = 3 or y = 5/2x -3/2 Slope of equation: 5/2 Slope of perpendicular equation: -2/5 Perpendicular equation: y --4 = -2/5(x -3) => 5y = -2x -14 Perpendicular equation in its general form: 2x+5y+14 = 0

The equation will be perpendicular to the given equation and have a slope of 3/4:- Perpendicular equation: y--3 = 3/4(x--2) => 4y--12 = 3x--6 => 4y = 3x-6 Perpendicular equation in its general form: 3x-4y-6 = 0

y=-x

Known equation: 5x-2y = 3 or y = 5/2x -3/2 Slope of known equation: 5/2 Slope of perpendicular equation: -2/5 Perpendicular equation: y- -4 = -2/5(x-3) => 5y =-2x-14 Perpendicular equation in its general form: 2x+5y+14 = 0

y = 1/3x+4/3

There is no name for it except "A line perpendicular to a line segment and passing through its midpoint".

Perpendicular equation: 4x +3y -5 = 0 Perpendicular slope: -4/3 Slope of line: 3/4 Point of line: (-2, -3) Equation of line: y - -3=3/4(x - -2) => 4y - -12=3x - -6 => 4y = 3x -6 Therefore the equation of the line is: 4y = 3x -6 or 3x -4y -6 = 0

y = -(1/5)x + 9