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?
+128408 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
