Hey, how do you know in a random question with 2 coordinates which is the x1 and y1 and which is the x2 and y2? I keep doing the x1/x2 and y1/y2 the wrong way round!
E.G. The line MN is the diameter of a circle, where M and N are (6,-4) and (0,-2) respectively. Find the radius of the circle
I know the forumla being the square root of (x2-x1)^2 + (y2-y1)^2...
But how on earth do you know from the question which is y2 and y1? I keep getting it wrong!
Thanks
Well I just tried it with the following:
X2: -2
X1: -4
Y2: 0
Y1: 6
I end up with the diameter being the square root of 40. Therefore, the radius is the square root of 20? It says the answer is the square root of 10!
Thanks for your help, but I am still stuck..
ok, here's how coordinates work. the first value in the pair are the x-values. so x1 and x2 are NOT -4 and -2, respectively. but technically, it also does not matter.
and
thus,
the radius is half of this, thus it is
so that was your mistake. 1/2 of sqrt(40) is NOT sqrt(20)
well, this hinges on the fact that we can write roots as powers.
we also know that
so, if we have , that is the same as
or equivalently,
so now on to your example. always look to factor out a number for which you know the square root of.
so, and we know the square root of four, that's just 2. so we end up with