If a segment has an endpoint at (3, 2) and the midpoint at (-1, 2), what are the coordinates of the other endpoint?

3 Answers
nat
Apr 22, 2018

#(-5,2)#

Explanation:

The distance from the midpoint to the first endpoint is #4#, which means that the other endpoint will be at the exact same distance from the midpoint as the first endpoint. So, four to the left of #(-1,2)# is #(-5,2)#

Barney V.
Apr 23, 2018

Coordinates of other endpoint#=-5,2#

Explanation:

Let the first endpoint be #A# and midpoint be #B# and other endpoint be #C#

Distance A to B:-

#:.=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#:.=sqrt(((-1)-(3))^2+(2-2)^2)#

#:.=sqrt((-4)^2+0#

#:.=sqrt(16)#

#:.=A to B=#4units#

The segment is a vertical line because the# y# values of
#A and B =2#

Coords of #B=-1,2#

The bearing of the line #B to C##=180^@#

#:.cos 180^@=-1xx4.0=-4# add to# x# coord of #B# then

#:.C#=-5#=x # coord.

#:.sin 180^@=0xx4.0=0# add to# y# coord of #B# then

#:.C#=2#=y# coord.

Coordinates of #C=-5,2#

Somebody N.
Apr 23, 2018

#color(blue)((-5,2)#

Explanation:

The coordinates of the midpoint of a line is given by:

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

Let the coordinates of the unknown end be:

#(x_2 , y_2)#

We know the coordinates of the midpoint are:

#(-1,2)#

So:

#((3+x_2)/2,(2+y_2)/2)#

And:

#(3+x_2)/2=-1=>x_2=-5#

#(2+y_2)/2=2=>y_2=2#

Coordinates:

#(-5,2)#

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