How does a transister amplify voltage???

Once in our class , our prof asked us, how exactly does a transister amplify the voltage given to base,that too to such high values?
The whole class was silent, no answers. I also tried to give some pathetic explanations.
However, here is some explanation to the same..
If you look at the BJT junction carefully,emitter is heavily doped and is smaller in size, so it gives a least resistance path for the current to flow.
The collector has moderate resistance and has large size compared to emitter, plus its reversed biased while operation, so it gives large resistance path for the current.
While the base is lightly doped and has very small area.
We know, Ie=Ic+Ib,
but Ib is very small so Ie is approximately equal to Ic.
But the base region is less resistance path , so current flows through it as such.

Transister Structure

But the collector region has high resistance and its reversed biased, so it forcibly draws more electrons from the supply, which collides with the particles of the collector thus, producing high voltage for the same current than emitter or base(the base hardly consumes 4-6 % of the total emitted electrons.
So the same current is flowing through the high resistance path as the emitter one, so it produces high voltage output, or ampified output.
Thus the voltage is amplified at the collector terminal terminal.

This also explains why output is taken from collector , rather than emitter while operating it as a amplifier.