Consider the line y=1 x -1 and the point P=(2,0).

(a) Write the formula for a function d(x) that describes the distance between the point P and a point (x, y) on the line. You final answer should only involve the variable x. Then d(x) =

(b) d'(x)=

(c) The critical number is x= .

(d) The closest point on the line to P is ( , ).

For the line and the point

1.    Let be the distance function for the distance between the point

      and the line .  The distance function will be

2.    To find the critical number, first find . Then, find the points at

       which

      but, only has complex solutions for . Therefore, the

      only critical point is

3.    To find the closest point on the line to P, find out if the critical point

      is a minimum point

       The closest point is

Another solved problem on distance between a point and a line can be found in the link: link

Step-by-step explanation:

d(x)=√((x-2)2+(y-0)²)

=√((x-2)²+y²)

=√((x-2)²+(x-1)²)

=√(x²-4x+4+x²-2x+1)

=√(2x²-6x+5)

D=d²(x)=2x²-6x+5

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y