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Interview practice maths

A ladder is resting along a wall at some angle x to the horizontal. A red line has been drawn along the middle of the ladder. When the ladder slides, what shape will be drawn out by the red line?

triangle

Original post by Ammar.M.

triangle

It has to be a curve

Reply 3

RDKGames

Study Forum Helper

Original post by olympiad1357

A ladder is resting along a wall at some angle x to the horizontal. A red line has been drawn along the middle of the ladder. When the ladder slides, what shape will be drawn out by the red line?

The shape that you seek is what we call an 'envelope' in differential geometry. The main feature is that no matter how much you slide the ladder, it will ALWAYS be tangent to this envelope.

We can formally determine the equation of this curve using parameterisation of the ladder's equation, but I'm assuming you've never comr across this hence are not expected to know it??

Reply 4

I hate maths!

Let the centre of the ladder have coordinates (x,y) and let the length of the ladder be the constant 2l. Can you find the relationship between x, y and l using geometry? This will tell you the shape drawn out by the centre of the ladder. Diagram in spoiler.

Spoiler

Reply 5

ab-sal

its always a quarter circle, whether it slides down or falls backwards. Mind Your Decision did a video on it on his youtube channel