Answer:
The shortest distance between the point (0, 2) and the line y = x + 5 is [tex]\frac{3}{\sqrt{2} }[/tex]
Step-by-step explanation:
The shortest distance d from a point ([tex]x_{0}[/tex],[tex]y_{0}[/tex]) to a line ax+by+c=0 can be found using the equation:
[tex]d=\frac{|ax_{0}+by_{0} +c| }{\sqrt{a^{2}+b^{2}}}[/tex]
Thus the shortest distance between (0,2) and y-x-5=0 is:
[tex]d=\frac{|-1*0+1*2 -5| }{\sqrt{-1^{2}+1^{2}} }[/tex] =[tex]\frac{3}{\sqrt{2} }[/tex]
