Question

Find points on the line x + y -4 = 0 which
are at one unit distance from the line
x + y - 2=0​

Answer 1

Answer:

I hope this helps you and sorry for the bad handwriting.

Answer 2

Number of points = 0

The given lines x + y -4 = 0 and x + y - 2=0 are parallel as both the given lines have equal slope(slope= -1).

For x + y -4 = 0 -

A = 1 , B = 1 , c1 = -4

For x + y - 2 = 0 -

A = 1 , B = 1 , c1 = -2

Distance between two parallel line , d = |c1 - c2|/√(A²+B²)

=> |-4 + 2|/√2

=> 2/√2

=> √2

The distance between the two lines is equal to √2 units , so no such point is possible that lies on x + y -4 = 0 is at one unit distance from the line

x + y - 2=0.