Final answer:
To find the coordinates of the other endpoint G, we can use the midpoint formula. By substituting the known values into the formula, we can solve for the coordinates of G. The coordinates of G are (7, 8).
Step-by-step explanation:
To find the coordinates of the other endpoint G, we need to use the midpoint formula. The formula for finding the midpoint of a line segment is (x, y) = [(x1 + x2)/2, (y1 + y2)/2].
In this case, the coordinates of endpoint H are (7, 13), and the midpoint is (7, 10.5). We can substitute these values into the midpoint formula and solve for the coordinates of endpoint G.
Using the equation (x, y) = [(x1 + x2)/2, (y1 + y2)/2], we have:
(x, y) = [(7 + x2)/2, (13 + y2)/2]
Substituting the known values, we get:
(7,10.5) = [(7 + x2)/2, (13 + y2)/2]
Multiplying both sides by 2 to get rid of the fractions, we get:
(14, 21) = (7 + x2, 13 + y2)
Now, we can compare the x-coordinate and y-coordinate separately.
For the x-coordinate, we have:
14 = 7 + x2
Solving for x2, we subtract 7 from both sides:
x2 = 14 - 7
x2 = 7
So, the x-coordinate of G is 7.
For the y-coordinate, we have:
21 = 13 + y2
Solving for y2, we subtract 13 from both sides:
y2 = 21 - 13
y2 = 8
So, the y-coordinate of G is 8.
Therefore, the coordinates of the other endpoint G are (7, 8).