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.
Hello the kopite
By symmetry, and are perpendicular, so in , with as base, the height of the triangle, .
Now , so the semi-perimeter, .
Area of (Did you know that formula?)
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 . Then .
Then there are two right-angled triangles, AEC and ECB, in which we can write an expression for (the distance CE). Using these, we get:
(Mind you, I think you should learn the 's' formula - it comes in useful!)