the midpoint of (line overtop of UV) UV is (5,-11). the coordinates of one endpoint are U(3,5). find the coordinates of endpoint V.
To find the coordinates of endpoint V, we need to use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that the midpoint of line segment UV is (5, -11) and one endpoint is U(3, 5), we can substitute these values into the formula and solve for the coordinates of endpoint V.
Let (x, y) represent the coordinates of endpoint V.
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
(5, -11) = ((3 + x) / 2, (5 + y) / 2)
Now, we can solve for x and y separately.
(x1 + x2) / 2 = (3 + x) / 2
5 = 3 + x
x = 5 - 3
x = 2
(y1 + y2) / 2 = (5 + y) / 2
-11 = 5 + y
y = -11 - 5
y = -16
Therefore, the coordinates of endpoint V are V(2, -16).