Find the shortest distance between the point (0,2) and the line y=x+5?

Answer 1

That is the line perpendicular to line y=x+5 and going through (0,2)
Find where they cross.

y=-x is a line perpendicular to it.
Now make it go through (0,2) y=-x+2
'calculate' where the two lines meet. (draw and read)
That is the point that has the shortest distance to (0,2)

Subtract the two points to get the vector.
Now unleach pythagoras to calculate the actual distance.