Question

Prove that the equations of the line x+y-1=0 and x-y-1=0 can be written as x+y=0 and x-y=0 by shifting the origin to a suitable point

Answer 1

If we shift the origin to (h,k)

The coordinates of the new system become

x' = x-h, y' = y-k

x' + h = x, y' + k = y

Now the given equations are

x+y -1=0

x-y-1=0

Adding them we get

2x-2=0

2x=2

x=1

Substituting in

x+y-1=0

1 + y -1 = 0

y=0

The point of intersection of the two lines is (1,0)

Shifting the origin to (1,0) we get

x' +1 = x, y'+0 = y

Substituting in x + y -1=0

x' + 1 +y' -1=0 => x' + y' = 0

Substituting in x -y-1=0

x' + 1 -y'-1 = 0 => x' -y'=0

Hence

The equations of the line x+y-1=0 and x-y-1=0 can be written as x'+y'=0 and x'-y'=0 by shifting the origin to (1,0)

Answer 2

Answer:3x-5y=0

Step-by-step explanation: