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)
