Triangle Problem

**aldrincabrera** · June 23rd 2011, 05:38 AM

Help me with this,.,.please

Given a triangle with vertices at A,B,C, show that the point R = 1/3 (A+B+C) lies on each of the medians. thnx

**Sudharaka** · June 23rd 2011, 07:00 AM

Originally Posted by aldrincabrera

Help me with this,.,.please

Given a triangle with vertices at A,B,C, show that the point R = 1/3 (A+B+C) lies on each of the medians. thnx

Dear aldrincabrera,

Take each median and find the point which divides it to the ratio 2:1 internally.

Intuition: As you may know your point R is the centroid of the triangle. The centroid divides each median to the ratio 2:1 internally.

**aldrincabrera** · June 23rd 2011, 07:03 AM

.,.ammm.,.i'm a bit confused.,.,can u show me just the beginning of the step???thnx.,.,

**Sudharaka** · June 23rd 2011, 07:19 AM

Originally Posted by aldrincabrera

.,.ammm.,.i'm a bit confused.,.,can u show me just the beginning of the step???thnx.,.,

Refer to the figure that I have attached. Take the median drawn from the point A as AD. Let $(x_a,y_a),(x_b,y_b)\mbox{ and }(x_c,y_c),$ be the coordinates of the vertices A,B and C respectively. Find the coordinates of D and then find the coordinates of E. I am sure you will be able to do this now.

**aldrincabrera** · June 23rd 2011, 07:27 AM

,.,.thank u so much sir,.,.this really helped me a lot

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