Question

The point (x,y) is on the graph f(x)=[root] x-3. L is the distance between point (x,y) and (4,0). Write an equation for L.

Answer 1

\[f(x)=\sqrt{x-3}\]

Answer 2

distance formula for this one
\[\sqrt{(x_2-x_1)^2+(y_x-y_1)^2}\] with \(x_1=x, x_2=4, y_1=\sqrt{x-3}, y_2=0\)

Answer 3

remember that the ecuation for distance between two points in the plane is:
\[d _{a \rightarrow b}=\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^{2}}\]

Answer 4

plug it in and get
\[\sqrt{(x-4)^2+(\sqrt{x-3})^2}\]

Answer 5

then some algebra inside the radical to clean it up a bit

Answer 6

And write it in function of L

Answer 7

thank you!