Given the distance from the point (2m, m-1) to the line x-y+3=0, d=2 find m.

The distance between a line ax+by+c = 0 and the point (x1,
y1) is:

|a*x1 + b*y1 + c|/sqrt (a^2 +
b^2)

Here the line is x - y + 3 = 0 and the point is (2m ,
m-1). The distance between them is 2

=> 2 = |2m -
(m-1) + 3|/sqrt (1 + 1)

=> 2 = |2m - m + 1 + 3|/sqrt
2

=> m+ 4 = 2*sqt 2 and m + 4 = -2*sqrt
2

=> m = 2*sqrt 2 - 4 and m = -2*sqrt 2 -
4

The values that m can take are 2*sqrt 2 - 4
and -2*sqrt 2 - 4