A sheet of paper is in the form of a triangle ABC in which AB=3, BC=4 and CA = 5. D is a point in AB such that AD = 1

The paper is folded so that C coincides with D and the resultant crease meets BC at the point X.

Find the length of BX.

I've made corrections in bold and brackets after each original incorrect part.

D3 looked ok at first glance but this is actually much easier.

Folding from one point to another just creates the perpendicular bisector of the segment connecting them.  So I just went with coordinates:

A=(0,3)
B=(0,0)
C=(5,0)[C=(4,0)]
D=(0,2)
X=(x,0) the x intercept of the perpendicular bisector of CD.
CD is a segment with slope -2/5[-1/2] and midpoint (5/2,1)[2,1]
so the crease is the line
y-1=(5/2)(x-5/2)[y-1=2(x-2)]
solve for x intercept
-1=(5/2)(x-5/2)[-1=2(x-2)]
x=-2/5 + 5/2[x=-1/2 + 2]
x=21/10[x=3/2]
X=21/10[X=3/2]
BX=21/10[BX=3/2]

Edited on April 2, 2014, 7:55 am

Posted by Jer on 2014-04-01 14:51:31