Determine the coordinates of points D,E and F divides BC into 4 congruent segments if the points B and C are (3,2) and (5,0) respectively. Check

Determine the coordinates of points D,E and F divides BC into 4 congruent segments if the  points B and C are (3,2) and (5,0) respectively. Check

B D E F C

The midpoint between B and C will be point E   ....it's coordinates will be  [ (3 + 5)/2 , (0 + 2)/2 ]  = [ 8/2, 2/2]  =  [4, 1]

The midpoint between B and E will be point D......its coordinates will be [ (4 + 3)/2 , ( 1 + 2)/2 ] = [7/2, 3/2]  =  [ 3.5, 1.5]

The midpoint between E and C will be point F.....its coordiantes will be [ (4 + 5)/2, (1 + 0)/2 ] = [ 9/2, 1/2]  = [ 4.5, 0.5 ]

Check  

Distance   between B,D  =   sqrt [ (3.5 -3)^2 + (1.5 - 2)^2]  =  sqrt [ 2 * 1/4]  = sqrt(2)/2  =   =   1/sqrt (2)

Distance between D,E   =   sqrt [ (3.5-4)^2 + (1.5 -1)^2] =  sqrt [ 2 * 1/4]  = sqrt(2)/2  =   =   1/sqrt (2)

Distance between E, F  =  sqrt [ (4 - 4.5)^2 + (1 -0.5)^2] = sqrt [ 2 * 1/4]  = sqrt(2)/2  =   =   1/sqrt (2)

Distance between F,C  =  sqrt [ ( 4.5 - 5)^2 + ( 0.5 - 0)^2 ] =  sqrt [ 2 * 1/4]  = sqrt(2)/2  =   =   1/sqrt (2)

And all the segments are congruent