whats the process behind solving these? Never seen them before i'm not sure where to start
P is a movable point on the line y=7-x
Find the coordinates of P when it is closest to the origin (0,0).
This is a really interesting question! What I'm going to do is give you some starting points, then why don't you let us know how far you get?
Firstly, you may remember that the straight-line distance between any two points is given by the equation:
which is secretly just Pythagoras' theorem in disguise. Because you don't know the exact points of P, you could actually pretend that it lies on the point x_2=x and y_2=y.
Another thing to think about is that closest and furthest have some synonyms that would normally raise alarm bells to any student studying differentiation - maybe you can use differentiation in some way, here?
EDIT: See below for some pointers on using a non-calculus approach - I tried to generalise for other curves, not just for straight lines, but their approach is WAY simpler and still worth knowing. Particularly if you're not up to differentiation, yet