Question

Find x, if the distance end points is (x,1) and (4,4) with the total distance is the square root of 10.

Answer 1

Okay, take a look at diagram 1 (I know it's rubbish I did it on paint :D), this shows all the information you've given in the question. The two coordinates and the distance between them.

Now if we draw additional lines on this diagram, we can make a right-angled triangle (this is on diagram 2). We can also work out the lengths of the additional sides because we know both coordinates at the end-points of the additional lines.

Finally because this is a right-angled triangle, Pythagoras' theorem must apply to its sides meaning
$( \sqrt{10} )^2 = (x-4)^2 + 3^2$
$10 = (x-4)^2 + 9$
$(x-4)^2 = 1 \Rightarrow x-4 = 1$
therefore x=5.