How do you find the missing coordinate if the 1st coordinate is C (6,5) has midpoint M (4,2)?

The formula to find the mid-point of a line segment give the two end points is:

#(x_M, y_M) = ((color(red)(x_1) + color(blue)(x_2))/2 , (color(red)(y_1) + color(blue)(y_2))/2)#

Where #(x_M, y_M)# is the midpoint and the given points are:

#(color(red)(x_1), color(red)(y_1))# and #(color(blue)(x_2), color(blue)(y_2))#

First, find the #x# value of the missing coordinate:

Substituting the information from the problem gives:

#4 = (color(red)(6) + color(blue)(x_2))/2#

We can now solve for #color(blue)(x_2)#:

#color(green)(2) xx 4 = color(green)(2)((color(red)(6) + color(blue)(x_2))/2)#

#8 = cancel(color(green)(2))((color(red)(6) + color(blue)(x_2))/color(green)(cancel(color(black)(2))))#

#8 = color(red)(6) + color(blue)(x_2)#

#-color(green)(6) + 8 = -color(green)(6) + color(red)(6) + color(blue)(x_2)#

#2 = 0 + color(blue)(x_2)#

#2 = color(blue)(x_2)#

#color(blue)(x_2) = 2#

First, find the #y# value of the missing coordinate:

Substituting the information from the problem gives:

#2 = (color(red)(5) + color(blue)(y_2))/2#

We can now solve for #color(blue)(y_2)#:

#color(green)(2) xx 2 = color(green)(2)((color(red)(5) + color(blue)(y_2))/2)#

#4 = cancel(color(green)(2))((color(red)(5) + color(blue)(y_2))/color(green)(cancel(color(black)(2))))#

#4 = color(red)(5) + color(blue)(y_2)#

#-color(green)(5) + 4 = -color(green)(5) + color(red)(5) + color(blue)(y_2)#

#-1 = 0 + color(blue)(y_2)#

#-1 = color(blue)(y_2)#

#color(blue)(y_2) = -1#

The coordinates of the Midpoint are: #(2, -1)#