The midpoint of UV is (5,-11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V. Show your work.
To find the coordinates of endpoint V, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint M(x, y) between two points A(x1, y1) and B(x2, y2) is given by:
x = (x1 + x2)/2
y = (y1 + y2)/2
In this case, we are given the midpoint M(5, -11), and one endpoint U(3, 5). Let's substitute these values into the midpoint formula to find the coordinates of endpoint V:
x = (3 + x2)/2 = 5
3 + x2 = 10
x2 = 10 - 3
x2 = 7
y = (5 + y2)/2 = -11
5 + y2 = -22
y2 = -22 - 5
y2 = -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 coordinates of the midpoint are the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Let's denote the coordinates of endpoint V as (x, y).
Using the midpoint formula, we have:
Midpoint x-coordinate = (x-coordinate of U + x-coordinate of V) / 2
5 = (3 + x) / 2
Now, we can solve this equation for x by multiplying both sides by 2 and subtracting 3:
10 = 3 + x
10 - 3 = x
7 = x
So, the x-coordinate of endpoint V is 7.
Moving on to the y-coordinate, we have:
Midpoint y-coordinate = (y-coordinate of U + y-coordinate of V) / 2
-11 = (5 + y) / 2
Again, we can solve this equation for y by multiplying both sides by 2 and subtracting 5:
-22 = 5 + y
-22 - 5 = y
-27 = y
So, the y-coordinate of endpoint V is -27.
Therefore, the coordinates of endpoint V are V(7, -27).
To find the coordinates of endpoint V, we can use the concept of the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the coordinates of the endpoints.
Given that the midpoint of UV is (5, -11) and one endpoint is U(3, 5), we can set up the following equation:
Midpoint = (Xm, Ym) = ((X1 + X2)/2, (Y1 + Y2)/2)
Plugging in the known values, we get:
(5, -11) = ((3 + X2)/2, (5 + Y2)/2)
Now, let's solve for X2 and Y2:
For X-coordinate:
5 = (3 + X2)/2
Multiply both sides of the equation by 2 to eliminate the fraction:
10 = 3 + X2
Subtract 3 from both sides of the equation:
7 = X2
For Y-coordinate:
-11 = (5 + Y2)/2
Multiply both sides of the equation by 2:
-22 = 5 + Y2
Subtract 5 from both sides of the equation:
-27 = Y2
Therefore, the coordinates of endpoint V are V(7, -27).
Note: The midpoint formula can also be applied if we know the coordinates of V and need to find the coordinates of U.