## elizabethann509 2 years ago How do I solve this for x? BD = 4x + 5 and BF = 9x

1. elizabethann509

|dw:1358121510552:dw| Not perfect but this is the drawing that goes with it

2. jim_thompson5910

are points G, E and F midpoints of the segments AB, BC and AC ?

3. elizabethann509

I think so? Something about a centroid? This is a question that I posted for my brother because he doesn't know how to do this. Everything should be even in the drawing but i'm not an expert artist or anything lol.

4. jim_thompson5910

if that's the case, then AE, GC, and BF are medians they all intersect at the centroid The distance from any vertex to the centroid is always twice as large as the distance from the centroid to the midpoint on the opposite segment (along the same median)

5. jim_thompson5910

what does this mean? it means that we can say BD = 2k DF = k for some number k |dw:1358122081547:dw|

6. jim_thompson5910

So BD = 2*DF 4x+5 = 2*9x solve for x, then use this to find BD and DF Your last step is to use them to find BF = BD + DF