Question

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

Answer 1

The shortest distance between the point (0, 2) and the line y = x + 5 is
`(3)/(√(2) )`

Explanation:

The shortest distance d from a point (
`x_(0)`,
`y_(0)`) to a line ax+by+c=0 can be found using the equation:

`d=\frac {\sqrt{a^(2)+b^(2)}}`

Thus the shortest distance between (0,2) and y-x-5=0 is:

`d=\frac-1*0+1*2 -5{\sqrt{-1^(2)+1^(2)} }` =
`(3)/(√(2) )`