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?

Guest Mar 27, 2019

#1**0 **

The centroid of a triangle will divide the triangle into 3 equal areas

The coordinates of the centroid are given by

;

( [sum of the x coordinates of the vertex points ] / 3 , [ sum of the y coordinates of the vertex points ] / 3 ) =

( [5 + 3 + 6 ] / 3 , [ 8 + -2 + 1 ] / 3 ) = ( 14/3, 7/3)

So

10m + n =

10 ( 14/3) + (7/3) = 140/3 + 7/3 = 147/3 = 49

CPhill Mar 27, 2019