The midpoint of is .
The coordinates of one endpoint
are . Find the coordinates
of endpoint V.
(2 points)
UV (5, −11)
U (3, 5)
To find the coordinates of endpoint V, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are the average of the x-coordinates and the average of the y-coordinates of the endpoints.
Given:
Midpoint M =
Endpoint U (x₁, y₁) = (3, 5)
Using the midpoint formula, we have:
M = ((x₁ + x₂)/2 , (y₁ + y₂)/2)
Since M is the midpoint and we know M = (5, -11), we can substitute the values into the formula:
(5, -11) = ((3 + x₂)/2 , (5 + y₂)/2)
Simplifying the equation, we have:
5 = (3 + x₂)/2
-11 = (5 + y₂)/2
Multiplying both sides of the equations by 2 to eliminate the denominators:
10 = 3 + x₂
-22 = 5 + y₂
Solving for x₂ and y₂:
x₂ = 10 - 3 = 7
y₂ = -22 - 5 = -27
Therefore, the coordinates of endpoint V are V(7, -27).