SOLUTION: Two vertical poles 2 metres and 8 metres high stand apart on a horizontal plane . the height in metres of the point of intersection of the lines joining the top of each pole to the

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Two vertical poles 2 metres and 8 metres high stand apart on a horizontal plane . the height in metres of the point of intersection of the lines joining the top of each pole to the      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 937906: Two vertical poles 2 metres and 8 metres high stand apart on a horizontal plane . the height in metres of the point of intersection of the lines joining the top of each pole to the bottom of the other pole is
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Cartesian system figure using coordinate geometry:

Bottom of the shorter pole on the origin so the top of this short pole is at point (0,2), bottom of short pole at (0,0).. The taller pole is k units to the right and has coordinates of its bottom (k,0) and the top, (k,8).

Line containing (0,2) and (k,0)
y=%28%280-2%29%2F%28k-0%29%29x%2B2
y=%282%2Fk%29x%2B2

Line containing (0,0) and (k,8)
y=%28%288-9%29%2F%28k-0%29%29x%2B0
y=%288%2Fk%29x

You must draw the graph of the segments for each pole and for the described lines on cartesian system to see this clearly.

You want the y value which satisfies both the lines.
(I have not finished solving this.)


.....
Do this: Solve each equation for x in terms of y. These will also contain k.
Now, equate the two formula expressions for x, and solve for y. You will find the k is a common factor of both sides. Find that highlight%28y=8%2F3%29