Precalculus, Chapter 10, 10.1, Section 10.1, Problem 60

Take note that the formula to determine the distance from a point (xo, yo) to a line Ax+By+C=0 is:
d = |Ax_o + By_o +C|/sqrt(A^2+B^2)
To apply, set one side of the given equation equal to zero.
y=x+2
0=x-y+2
Then, plug-in the coefficients of x and y, as well as the constant to the formula.
d=|1x_0 + (-1)y_o +2|/sqrt(1^2+(-1)^2)
d=|x_o -y_o + 2|/sqrt2
And, plug-in the given point (2,1).
d=|2-1+2|/sqrt2
d=|3|/sqrt2
d=3/sqrt2
d=3/sqrt2*sqrt2/sqrt2
d=(3sqrt2)/2
Therefore, the distance between the point (2,1) and the line y=x+2 is (3sqrt2)/2 units.