Amath Q

renz

The figure shows a triangle ABC.
A rectangle EFGH is inscribed in the triangle.
Let B,C be the point (a,0) and (b,h) respectively, HE=t
(a) Find the coordinates of H and G in terms of a,b,h,t
(b) Find the equation of the locus of the intersecting point of diagonals of the rectangle, as t varies.

計到H (bt/h , t)
跟著我計G
Let G be (k,t)
t/h = (k-b)/(a-b)
k= t(a-b)/h +b

但ans 就是 a+t(b-a)/h
b part我就未開始計，想睇下a part錯咩先，謝

unlock-YM

The figure shows a triangle ABC.
A rectangle EFGH is inscribed in the triangle.
Let B,C be the point (a,0) and (b,h) respectively, HE=t
(a) Find the coordinates of H and G in terms of a,b,h,t
(b)  ...
renz 發表於 3/4/2010 06:05 PM

t/h =(a-k)/(a-b)
h(a-k) = t(a-b)
-k = t(a-b)/h - a
k = a + t(b-a)/h

[GW]赤沙

我想問下b part個答案係咪 2hx - (4b-2a) y + ha = 0?