The midpoint of segment AB is (1, 4). The coordinates of point A are (2,-3). How do you find the coordinates of point B?

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Answer 1 · 2016-12-31T09:09:10

The coordinates of point B are #(0,11)#

Midpoint of a segment, whose two end points are #A(x_1,y_1)# and #B(x_2,y_2)# is

#((x_1+x_2)/2,(y_1+y_2)/2)#

as #A(x_1,y_1)# is #(2,-3)#, we have #x_1=2# and #y_1=-3#

and a midpoint is #(1,4)#, we have

#(2+x_2)/2=1#

i.e. #2+x_2=2# or #x_2=0#

#(-3+y_2)/2=4#

i.e. #-3+y_2=8# or #y_2=8+3=11#

Hence coordinates of point #B# are #(0,11)#