if A(1,4) B(2,-3) C(-1,-2) are the vertices of a triangle ABC. find
a) the equation of the median through A
b) the equation of altitude through B
c) the right bisector of BC
given A(1,4), B(2,-3) and C(-1,-2) are the vertices of the triangle ABC.
(a)
median through A will pass through the mid-point of BC.
let D is the mid-point of BC.
the coordinates of the mid-point of BC is
since the median AD will pass through the points A and D.
the equation of a line passing through two points A(1,4) and is:
therefore the equation of the median through A is 13x-y=9
(b) the equation of the altitude through B is a line perpendicular to AC.
and passes through B.
slope of the straight line AC
slope of the line perpendicular to AC
since it passes through B(2,-3).
equation of the straight line with slope -1/3 and passes through a given point B(2,-3):
therefore the equation of the altitude through B is x+3y+7=0
(c) the right bisector of BC passes through the mid-point of BC and is perpendicular to BC.
the coordinates of the mid-point of BC is .
the slope of line BC =
the slope of the line perpendicular to BC is 3.
equation of the straight line with slope 3 and passes through the given points is:
therefore the equation of the right bisector of BC is 3x-y=4