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 $(0,11)$