looks like coordinate geometry but is not really...

The points A and B have coordinates (3,-1) and (6,3) respectively. The points C and D are each distant 4 units from A and 6 units from B, forming a kite. Show that the length of CD is 3 x root of 7 (i dont get how you people manage to type math symbols).

I figured that this is supposed to be dealed with using the cosine rule and not by trying to calculate the coordinates of C and D, which would take ages. I managed to get the right answer, which is 7.blablablabla, but not in the right form, that is in decimal form instead of surd form. I really can't figure out how to get a direct surd. (Headbang)

Alternative to 's' formula

Quote:

Originally Posted by

**the kopite** ok thanks, that clears things up. i just didnt know the math wizards made typos...

'Fraid so!

Grandad

PS

If you want an alternative that doesn't use the 's' formula, how about this?

Suppose AB and CD meet at E, and the length $\displaystyle AE = x$. Then $\displaystyle EB = 5-x$.

Then there are two right-angled triangles, AEC and ECB, in which we can write an expression for $\displaystyle h$ (the distance CE). Using these, we get:

$\displaystyle h^2 = 4^2 - x^2 = 6^2 - (5-x)^2$

$\displaystyle \Rightarrow 16-x^2 = 36-25+10x-x^2$

$\displaystyle \Rightarrow 10x = 5$

$\displaystyle \Rightarrow x = \tfrac12$

$\displaystyle \Rightarrow h^2 = 16 - \tfrac14 = \frac{63}{4}$

$\displaystyle \Rightarrow h = \frac{3\sqrt7}{2}$

(Mind you, I think you should learn the 's' formula - it comes in useful!)