Points: (-4, 8) and (0, -2)
Slope: (8--2)/((-4-0) = -5/2
Perpendicular slope: 2/5
Midpoint: (-4+0)/2, (8-2)/2 = (-2, 3)
Equation: y-3 = 2/5(x--2)
Multiply all terms by 5: 5y-15 = 2(x--2) => 5y = 2x+19
Perpendicular bisector equation in its general form: 2x-5y+19 = 0
Points: (-2, 3) and (1, -1) Midpoint: (-0.5, 1) Slope: -4/3 Perpendicular slope: 4/3 Equation: 3y = -4x+1 Perpendicular bisector equation: 4y = 3x+5.5
Points: (s, 2s) and (3s, 8s) Midpoint: (2s, 5s) Slope: 3 Perpendicular slope: -1/3 Perpendicular equation: y -5s = -1/3(x -2s) => 3y = -x +17s Perpendicular bisector equation in its general form: x +3y -17s = 0
Points: (7, 3) and (-6, 1) Midpoint: (0.5, 2) Slope: 2/13 Perpendicular slope: -13/2 Perpendicular equation: y-2 =-13/2(x-0.5) => 2y-4 = -13x+6.5 => 2y = -13x+10.5 Therefore the perpendicular bisector equation is: 2y = -13x+10.5
To find the perpendicular bisector of a line segment, first, determine the midpoint of the segment by averaging the x-coordinates and y-coordinates of the endpoints. Next, calculate the slope of the line segment and find the negative reciprocal of that slope to get the slope of the perpendicular bisector. Then, use the midpoint and the new slope to write the equation of the perpendicular bisector in point-slope form. Finally, you can convert it to slope-intercept form if needed.
Points: (3, 5) and (7, 11) Midpoint: (5, 8) Slope: 3/2 Perpendicular slope: -2/3 Perpendicular equation: y-8=-2/3(x-5) => 3y-24=-2x+10 => 3y=-2x+34 Therefore the perpendicular bisector equation is: 3y = -2x+34
Points: (-2, 3) and (1, -1) Midpoint: (-0.5, 1) Slope: -4/3 Perpendicular slope: 4/3 Equation: 3y = -4x+1 Perpendicular bisector equation: 4y = 3x+5.5
Points: (-1, 4) and (3, 8) Midpoint (1, 6) Slope: 1 Perpendicular slope: -1 Perpendicular bisector equation: y-6 = -1(x-1) => y = -x+7
Points: (-2, 5) and (-8, -3) Midpoint: (-5, 1) Slope: 4/3 Perpendicular slope: -3/4 Perpendicular equation: y-1 = -3/4(x--5) => 4y = -3x-11 Perpendicular bisector equation in its general form: 3x+4y+11 = 0
Points: (s, 2s) and (3s, 8s) Midpoint: (2s, 5s) Slope: 3 Perpendicular slope: -1/3 Perpendicular equation: y -5s = -1/3(x -2s) => 3y = -x +17s Perpendicular bisector equation in its general form: x +3y -17s = 0
End points: (-2, 4) and (-4, 8) Midpoint: (-3, 6) Slope: -2 Perpendicular slope: 1/2 Perpendicular bisector equation: y -6 = 1/2(x--3) => y = 0.5x+7.5
Points: (7, 3) and (-6, 1) Midpoint: (0.5, 2) Slope: 2/13 Perpendicular slope: -13/2 Perpendicular equation: y-2 =-13/2(x-0.5) => 2y-4 = -13x+6.5 => 2y = -13x+10.5 Therefore the perpendicular bisector equation is: 2y = -13x+10.5
Endpoints: (-4, -10) and (8, -1) Midpoint: (2, -5.5) Slope: 3/4 Perpendicular slope: -4/3 Perpendicular equation: y --5.5 = -4/3(x-2) => 3y = -4x -8.5 Perpendicular bisector equation in its general form: 4x+3y+8.5 = 0
To find the perpendicular bisector of a line segment, first, determine the midpoint of the segment by averaging the x-coordinates and y-coordinates of the endpoints. Next, calculate the slope of the line segment and find the negative reciprocal of that slope to get the slope of the perpendicular bisector. Then, use the midpoint and the new slope to write the equation of the perpendicular bisector in point-slope form. Finally, you can convert it to slope-intercept form if needed.
Endpoints: (3, 5) and (7,7) Midpoint: (5, 6) Slope: 1/2 Perpendicular slope: -2 Perpendicular bisector equation: y-6 = -2(x-5) => y = -2x+16
Endpoints: (-7, -3) and (-1, -4) Midpoint: (-4, -3.5) Slope: (-3--4)/(-7--1) = -1/6 Perpendicular slope: 6 Perpendicular bisector equation: y--3.5 = 6(x--4) => y = 6x+20.5
Points: (3, 5) and (7, 11) Midpoint: (5, 8) Slope: 3/2 Perpendicular slope: -2/3 Perpendicular equation: y-8=-2/3(x-5) => 3y-24=-2x+10 => 3y=-2x+34 Therefore the perpendicular bisector equation is: 3y = -2x+34
It works out in its general form as: x+3y-17s = 0