Ladder problem
Geometry
Level
2
A ladder is laying vertically on a wall. this is a weird ladder, since it has wheels on the bottom, so the ladder slides down and hits the ground. In what path does the midpoint of the ladder travel?
In a straight line
in a squiggly line
in 2 straight lines
In a quarter circle
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Let the length of the ladder be l and the coordinates of the midpoint of the ladder be ( x , y ) with the origin at the bottom of the wall. We note that when the ladder slides down, the relationship x 2 + y 2 = ( 2 l ) 2 is always true and it is the first quadrant with origin as its centre.