[tex]\boxed{D=\sqrt{2}}[/tex]
The Shortest Distance from a point to a line is the perpendicular distance from the point to the line. in other words, this is the line segment joining the point to the line in a perpendicular way.
Suppose you have a line written in General Form as:
[tex]ax+bx+c=0 \\ \\ a,b,c \ Real \ Constants[/tex]
And a point:
[tex](x_{0},y_{0})[/tex]
Then, the Shortest Distance can be found as follows:
[tex]D=\frac{\mid ax_{0}+by_{0}+c \mid}{\sqrt{a^2+b^2}} \\ \\ Writting \ x - y = -1 \ in \ General \ Form: \\ \\ x-y+1=0 \\ \\ So: \\ \\ a=1 \\ b=-1 \\ c=1 \\ \\ And: \\ \\ (x_{0},y_{0})=(2,1) \\ \\ \\ So: \\ \\ D=\frac{\mid (1)(2)+(-1)(1)+1 \mid}{\sqrt{1^2+(-1)^2}} \\ \\ D=\frac{\mid 2-1+1 \mid}{\sqrt{2}} \\ \\ D=\frac{2}{\sqrt{2}} \\ \\ D=\frac{2}{\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}} \\ \\ Finally: \\ \\ \boxed{D=\sqrt{2}}[/tex]
Distance Formula: https://brainly.com/question/10134840
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