Question

Point B is at (3,1). For which segment is B a midpoint?
AC¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(8,6)
AC¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(5,3)
AD¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(6,4)
AC¯¯¯¯¯¯¯¯ with endpoints at A(1,−1) and C(7,5)

Answer 1

well, you could test each option and find their midpoints
or
you could let the other endpoint be (x,y)(3,1)
then ( (x+1)/2 , (y-1)/2) = (3,1)

(x+1)/2 = 3 ---> x = 5
(y-1)/2 = 1 ----> y = 3

Answer 2

thank you!

Answer 3

A(1. -1), B(x, y), C(5, 3).
x-1 = 1/2(5-1)
X = 3.

y+1 = 1/2(3+1)
Y = 1.