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

**
**