A(0,0) B(3,y1) C(3,y2)

We do not know what numbers y1 and 
y2 stand for.  But look at their first coordinates.  They are the 
same number 3.  Let's pick some test values out the for y1 and y2,
say y1=2 and y2=-3

   

Now notice that we can draw a vertical line (in green through both
of those 2 points.   

   

Now you can see that it didn't matter
which numbers we picked for y1 and y2 
to stand for, they would always be on 
that green line. 

IOW, the points B(3,y1) and C(3,y2) will
both be located somewhere on that same 
green line, regadless of what y1 and y2
are.

Now we can use the distance formula to find the NEAREST
distance from A(0,0) to the green line.

What point will we choose on the green line to find the 
distance to?  The point on the x-axis, which has to have 
x-coordinate 3, and the point on the green line closest
to (0,0) is the point (3,0).

   

So we use the distance formula:

 distance formula, where 
d =   
where (x1,y1) = (0,0)and where (x2,y2) = (3,0)

d =  =  = 3

So it's 3 units from (0,0) to its closest point on the 
green line.  Of course we could have just counted the 
marks and have known it was 3 units from the origin over 
to the green line without even bothering with the 
distance formula.  But we were told to use the distance
formula.

Edwin