Each point on the line can be expressed as a coordinate in the form...
.
Why? A coordinate is of the form and
So what to do is think in terms of Pythagoras triangle... You have two sides, one of length , one of length and one unknown side that you must find.
Why? Well just think of the coordinate as being distance along the x-axis then distance up to get to the point. This will form a right angled triangle with side lengths and
So, let's call this unknown side , using the standard Pythagoras formula we get...
Now you finish this off by expanding everything and you will be left with a formula of the form...
then just take square roots to get,
which will be your answer.
Well you want to find the value of that makes that function the smallest.
This will happen at one of two places.
A critical point,
An end point of the range of . (i.e. ).
Immediately you can see that that if then (if not I'll explain).
So that leaves you to find critical points...
I'll start you off...
If
=> .
Solve for this to be 0 and what does that tell you..?