Triangle $ABC$ has vertices at $A(5,8)$, $B(3,-2)$, and $C(6,1)$. The point $D$ with coordinates $(m,n)$ is chosen inside the triangle so that the three small triangles $ABD$, $ACD$ and $BCD$ all have equal areas. What is the value of $10m + n$?

Answer 1

as discussed in Method III here,

http://jwilson.coe.uga.edu/emt668/EMAT6680.2000/Lehman/emat6690/trisecttri's/trisect.html

your point D will be the centroid of ABC. To find the centroid, read here:

http://www.mathopenref.com/coordcentroid.html

Answer 2

Thanks :)

Answer 3

Triangle ABC with vertices A(3,2), B(5,4), C(5, 8) is translated (x-6, y-5). What are the coordinates of triangle A’B’C’?