How to find the equation of a perpendicular in a triangle?

Question

Triangle ABC, you have to find the perpendicular bisector of BC.

Answer 1

1.find the midpoint of BC usingthe midpoint formula
(x1+x2/2,y1+y2/2) say (x,y)
2.find the slope os BC using theformula
y2/y1/x2-x1 say m
3.the slope of the perpendicular bisector will be the negative inverse of this -1/m
4. now use the point (x,y) and slope (-1/m) and find the equation of the perpendicular bisector

Answer 2

take the points of BC and find the slope
take the negative reciprocal of the slope and use the median of B and C to find the new equation
e.g. if the slope is 3, then the negative recriprocal would be -1/3
use the formula y = mx + b to find the y-intercept

e.g. if the points for B and C were (1,2) and (4,8)

find the slope
(8-2)/(4-1) = 2
the negative reciprocal would be -1/2

the median for B and C
(1 + 4)/2 = 5/2
(2 + 8)/2 = 5
(5/2, 5)

use the equation y = mx + b to find the y-intercept (or b)
x = 5/2
y = 5
m = -1/2
5 = (-1/2)(5/2) + b
b = 25/4

thus the equation is y = (-1/2)x + 25/4

Answer 3

a squared + b squared = c squared, where c is the hypoteneuse and a and be are legs
the triangle you describe will have points a,b,c,d with d being the midpoint of ac.
by defuinition this triangle has to have two legs of equal length.
therefore seg ad must be the shortest, the vert the long leg and ab the hyp.
c squared = (ad) squared plus (bc) squared.
put the values for c in and ad. do the math
take the square root of the difference of the squares c and ad
what a helluva writing assignment the math is easy, the writing was tough. thanks for the challenge.

Answer 4

the equation of the perpendicular is the inverse of the line it is intersecting. to bisect the line use the equation (X1+X2/2, Y1+Y2)