Question

The vertices of ΔPQR are P (2, 1), Q (–2, 3) and R (4, 5). Find equation of the median through the vertex R.

Answer 1

The vertices of triangle are P( 2,1 ) , Q( −2,3 ) and R( 4,5 ) .

Let RM be the median drawn from vertex R to the side PQ. Thus, M is the mid-point of line PQ.

Let ( m,n ) be the coordinates of mid-point M.

The formula for the mid-point ( m,n ) of two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

( m,n )= x 1 + x 2 2 , y 1 + y 2 2 (1)

Substitute ( 2,1 ) for ( x 1 , y 1 ) and ( −2,3 ) for ( x 2 , y 2 ) in equation (1).

( m,n )=( 2+−2 2 , 1+3 2 ) =( 0 2 , 4 2 ) =( 0,2 )

The formula for the equation of line passing through the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by,

( y− y 1 )= y 2 − y 1 x 2 − x 1 ⋅( x− x 1 ) (2)

Substitute ( 0,2 ) for ( x 1 , y 1 ) and ( 4,5 ) for ( x 2 , y 2 ) in equation (2).

( y−2 )= 5−2 4−0 ⋅( x−0 ) ( y−2 )= 3 4 ( x−0 ) 4( y−2 )=3x 4y−8=3x

Rearrange the terms in above equation.

3x−4y+8=0

Thus, the equation of median passing through the vertex R is 3x−4y+8=0 .