Answer to Question #221381 in Geometry for helpme

Question

Walking down a hallway in the school, you notice that the library is halfway between the canteen and the Science Laboratory. The Science Laboratory is halfway between the library and the computer laboratory. Prove that the distance between the entrances of the canteen and library is the same as the distance between the entrances of the science laboratory and computer laboratory

Answer 1

Let's define points for ease:

Canteen - point A

Library - point B

Science Laboratory - point C

Computer Laboratory - point D

We need to prove that AB = CD.

Given, if AC is x long, then, as the library is halfway between the canteen and the Science Laboratory, AB = BC = x/2.

Given, if BD is y long, then, as the Science Laboratory is halfway between the library and the computer laboratory, BC = CD = y/2.

Thus, BC = x/2 = y/2, so x = y.

That means AC (which is x) is equal to BD (which is y).

Having that, AB (x/2) and CD (y/2) are equal.