from the question, we know that one of the endpoints of the line segment is (x+2, 1/4y)
the midpoint of the line segment is (6, -3)
and we were told to find the coordinates in terms of x and y
so, lets used the midpoint formular
M = (x1+x2/2, y1+y2/2)
since the midpoint is (6, -3)
lets substitute it for M:
(6, -3) = (x1+x2/2, y1+y2/2)
X-coordinates
6 = x1 + x2/2
recall that one of the endpoints is (x+2, 1/4y). So lets make (x+2, 1/4y) be our (x1, y1).
lets substitute x + 2 for x1.
6 = (x+2)+x2/2
solving for our second x-coordinates x2.
multiply both sides by 2
12 = x + 2 + x2
subtract 2 from both sides
10 = x + x2
subtract x from both sides. Therefore , the x-coordinate of our second point is
x2 = -x + 10
Y-coordinate
-3 = y1 + y2/2
lets substitute 1/4y for y1
-3 = 1/4y + y2/2
to solve for y2, lets multiply both sides by 2
-6 = 1/4y + y2
subtract 1/4y from both sides
y2 = -1/4y - 6
therefore, the other coordinate expressed in terms of x and y is:
(-x + 10, -1/4y - 6)