The midpoint of UV is (5, -10). The coordinates of one endpoint are U(3,6). Find the coordinates of endpoint V.
xu and yu = coordinates of point U
xu = 3 y , yu = 6
xv and yv = coordinates of point V
xm and ym = coordinates of point midpoint
xm = 5 , ym = - 10
xm = ( xu + xv ) / 2
5 = ( 3 + xv ) / 2
Muliply both sides by 2
10 = 3 + xv
Subtract 3 to both sides
7 = xv
xv = 7
ym = ( yu + yv ) / 2
- 10 = ( 6 + yv ) / 2
Muliply both sides by 2
- 20 = 6 + yv
Subtract 6 to both sides
- 26 = yv
yv = - 26
Coordinates of point V:
( 7 , - 26 )
To find the coordinates of endpoint V, we'll use the midpoint formula, which states that the midpoint of a line segment is the average of the coordinates of its endpoints.
Given that the midpoint of UV is (5, -10) and one endpoint is U(3, 6), let's denote the coordinates of endpoint V as (x, y).
According to the midpoint formula, the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
Thus, we can write two equations based on the midpoint formula:
1. (x1 + x2) / 2 = x
2. (y1 + y2) / 2 = y
Plugging in the known values, we can set up the equations as follows:
1. (3 + x) / 2 = 5
2. (6 + y) / 2 = -10
Solving these equations will give us the values of x and y, which are the coordinates of endpoint V.
Let's solve equation 1 first:
(3 + x) / 2 = 5
Multiplying both sides of the equation by 2:
3 + x = 10
Subtracting 3 from both sides of the equation:
x = 7
Now, let's solve equation 2:
(6 + y) / 2 = -10
Multiplying both sides of the equation by 2:
6 + y = -20
Subtracting 6 from both sides of the equation:
y = -26
Therefore, the coordinates of endpoint V are (7, -26).