Points: (2, 5) and (11, 17)
Midpoint: (6.5, 11)
Slope: 4/3
Perpendicular slope: -3/4
Perpendicular equation: y-11 = -3/4(x-6.5) => 4y = -3x+63.5
In its general form: 3x+4y-63.5 = 0
Points: (13, 19) and (23, 17) Midpoint: (18, 18) Slope: -1/5 Perpendicular slope: 5 Perpendicular equation: y-18 = 5(x-18) => y = 5x-72
The endpoints of a line segment graphed on a Cartesian coordinate system are (2, -5) and (-4, 2). What are the coordinates of the midpoint of the segment?
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: (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 = -13x+10.5
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: (-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
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
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
8
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