Question

Prove that the coordinates, x and y, of the middle point of the line joining the point (2, 3) to the point (3, 4) satisfy the equation, x – y + 1 = 0

Answer 1

The coordinates of the midpoint of the line joining (2,3) and (3,4) are

(x,y)  =  [ (2+3)/2 , (3+4)/2 ]
∴(x,y) = (5/2 , 7/2)

Putting x = 5/2  and y = 7/2 in the LHS of equation:

x - y + 1
=5/2 - 7/2 + 1
=-2/2 + 1
=-1 + 1
=0
=RHS

Hence proved

Answer 2

Let (x1,y1)=(2,3) and (x2,y20=(3,4) and the midpoint be P(x,y).

Then,

P(x,y)= (2+3/2 , 3+4/2)

           =(5/2 , 7/2)

  Using these coordinates in the given equation

x-y+1=5/2-7/2+1=0

L.H.S=R.H.S

Hence proved.