Question

Find the equation of the perpendicular bisector of the line joining the points (3,8) and (2,-5)?

Answer 1

find the midpoint of the given line

the bisector is perpendicular
... so its slope is the negative-reciprocal of the given line

use point-slope to write the equation

Answer 2

A(3, 8), M(x,y), B(2, -5).
m1 = (-5-8)/(2-3) = -13/-1 = 13.
m2 = -1/13,

x-3 = 2-x,
X = 2.5.

y-8 = -5-y,
Y = 1.5.

(2.5, 1.5),
Y = mx + b,
1.5 = (-1/13)2.5 + b,
b = 1.692.
Eq: Y = (-1/13)x + 1.692.

Answer 3

m=y2-y1/x2-x1
m1=13
since lines are perpendicular m1m2=-1
m2=-1/13
using formula Y-Y1=m(X-X1)
Substite any of the points
Y-8=-1/13(X-3)
open bracket
y-8=-x/13+3/13
13y-104=-x+3
13y+x-104-3=0
13y+x-107=0

Answer 4

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