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# Points $A$, $B$, $C$, and $D$ are located on a line. $A$ is at $(-6,13)$, $D$ is at $(2, 14)$, $C$ is the midpoint of $\overline{AD}$ and \$B

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Points A, B, C, and D are located on a line. A is at (-6,13), D is at (2,14), C is the midpoint of AD and B is the midpoint of AC. What is the sum of the coordinates of point B? Express the answer as a common fraction.

Aug 15, 2019

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A = (-6,13)     D = (2,14)

So.....using the midpoint fomula.....C  must be

[(-6 + 2) /2, (14/+13)/2 ]   =  [ -4/2, 27/2]   = ( -2, 27/2 )

And....using the midpoint fomula once  more.... B must be

[ (-6 + -2)/2 , ( 27/2 + 13)/2 ]  =  [ ( -4, ( 53/2)/2 ] =  ( -4, 53/4)

So...the sum of the  coordinates of B   =  -4 + 53/4  =    (-16 + 53) /4   =  37/4

Aug 15, 2019