Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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 can use the midpoint formula:
Midpoint formula:
For a line segment with endpoints (x1, y1) and (x2, y2), the coordinates of the midpoint (M) are given by:
M = ((x1 + x2)/2, (y1 + y2)/2)
We are given that the midpoint M is (5, -11) and one endpoint U is (3, 5). Let's plug in these values into the midpoint formula and solve for V:
M = ((3 + x2)/2, (5 + y2)/2)
(5, -11) = ((3 + x2)/2, (5 + y2)/2)
Using the fact that M is (5, -11), we can write two separate equations for the x and y coordinates:
5 = (3 + x2)/2 --> equation 1
-11 = (5 + y2)/2 --> equation 2
To solve for x2, we can multiply both sides of equation 1 by 2:
10 = 3 + x2
Subtracting 3 from both sides gives us:
7 = x2
Therefore, the x-coordinate of endpoint V is 7.
To solve for y2, we can multiply both sides of equation 2 by 2:
-22 = 5 + y2
Subtracting 5 from both sides gives us:
-27 = y2
Therefore, the y-coordinate of endpoint V is -27.
Therefore, the coordinates of endpoint V are (7, -27).