The midpoint of #UV# is #(5,-11)#. The coordinates of one endpoint are #U(3, 5)#. What are the coordinates of endpoint #V#?

1 Answer
jags
Jul 3, 2016

Co-ordinates of #V = (7, -27)#

Explanation:

Midpoint of points AB where #A = (x_1, y_1)# and #B = (x_2,y_2)# is represented as #((x_1+x_2)/2, (y_1 + y_2)/2)#

In our case #U = (3,5#) and midpoint of #UV = (5,-11)#. Let #V = (x_2, y_2)#

# (x_1+x_2)/2 = 5# => # (3+x_2)/2 = 5# => #3+x_2 = 10# => # x_2 = 7#

# (y_1+y_2)/2 = -11# => # (5+y_2)/2 = -11# => #5+y_2 = -22# => # y_2 = -27#

#V = (7, -27)#

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