The midpoint of 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 determine the change in x and the change in y from U to V.
The change in x is found by subtracting the x-coordinate of U (3) from the x-coordinate of the midpoint (5):
Change in x = 5 - 3 = 2
Similarly, the change in y is found by subtracting the y-coordinate of U (5) from the y-coordinate of the midpoint (-11):
Change in y = -11 - 5 = -16
Now, we can add the change in x and the change in y to the x-coordinate and y-coordinate of the midpoint, respectively, to find the coordinates of endpoint V:
V(x, y) = (Midpoint(x) + Change in x, Midpoint(y) + Change in y)
V(x, y) = (5 + 2, -11 - 16)
V(x, y) = (7, -27)
Therefore, the coordinates of endpoint V are V(7, -27).
To find the coordinates of endpoint V, we can use the midpoint formula. The midpoint formula states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the coordinates:
((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we know the midpoint of UV is (5, -11), and one endpoint is U(3, 5). Let's use these values to solve for the coordinates of endpoint V.
Let the coordinates of endpoint V be (x, y).
Using the midpoint formula, we can set up the following equations:
((3 + x) / 2, (5 + y) / 2) = (5, -11)
From the x-coordinate equation:
(3 + x) / 2 = 5
Solve for x by multiplying both sides of the equation by 2:
3 + x = 10
Subtract 3 from both sides to isolate x:
x = 7
From the y-coordinate equation:
(5 + y) / 2 = -11
Solve for y by multiplying both sides of the equation by 2:
5 + y = -22
Subtract 5 from both sides to isolate y:
y = -27
Therefore, the coordinates of endpoint V are V(7, -27).
To find the coordinates of endpoint V given the midpoint and one endpoint, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment are equal to the average of the coordinates of its endpoints.
Let's denote the coordinates of endpoint V as (x, y).
According to the midpoint formula:
(x-coordinate of U + x-coordinate of V) / 2 = 5
(3 + x) / 2 = 5
To find the value of x, we can solve the equation:
3 + x = 2 * 5
3 + x = 10
x = 10 - 3
x = 7
Now, let's find the value of y.
(y-coordinate of U + y-coordinate of V) / 2 = -11
(5 + y) / 2 = -11
To find the value of y, we can solve the equation:
5 + y = 2 * -11
5 + y = -22
y = -22 - 5
y = -27
Therefore, the coordinates of endpoint V are (7, -27).