Sorry to bring this up again but could I get help on this problem?

https://web2.0calc.com/questions/medians-ax-and-by-of-triangle-abc-are-perpendicular

Thanks so much!

AnonymousConfusedGuy
Mar 12, 2018

#1**0 **

Extend the line CG through to meet AB at Z (say).

The medians of a triangle intersect at a point, so CZ will be the third median, so Z will be the midpoint of AB.

Show that ZG is half the length of AB.

(The easiest way to do this is to draw a line from Z, parallel to AY to meet the line BG. Since Z is the midpoint of AB,

this line will bisect BG. Then consider the small right-angled triangle having ZG as its hypotenuse, use Pythagoras.)

Having done that, use the 1/3, 2/3 property for the median CZ.

Tiggsy

Guest Mar 12, 2018