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 formula for finding the midpoint of a line segment. The formula states that the midpoint (M) of a line segment with endpoints (x1, y1) and (x2, y2) is:
M = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we are given that the midpoint of UV is (5, -11) and one endpoint is U (3, 5). Let's substitute these values into the equation and solve for the coordinates of endpoint V.
M = ((x1 + x2) / 2, (y1 + y2) / 2)
(5, -11) = ((3 + x2) / 2, (5 + y2) / 2)
To solve for x2, we can multiply both sides of the equation by 2 and then subtract 3 from both sides:
2 * 5 = 3 + x2
10 - 3 = x2
7 = x2
To solve for y2, we can multiply both sides of the equation by 2 and then subtract 5 from both sides:
2 * (-11) = 5 + y2
-22 - 5 = y2
-27 = y2
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 between two points (x₁, y₁) and (x₂, y₂) are given by the averages of the respective coordinates:
Midpoint (x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
We are given the midpoint of UV as (5, -11), and one endpoint U as (3, 5).
Let's plug these values into the midpoint formula and solve for the coordinates of endpoint V:
Midpoint (x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
(5, -11) = ((3 + x₂)/2, (5 + y₂)/2)
Now, let's solve for x₂ and y₂:
(3 + x₂)/2 = 5 --> Multiply both sides by 2
3 + x₂ = 10 --> Subtract 3 from both sides
x₂ = 7
(5 + y₂)/2 = -11 --> Multiply both sides by 2
5 + y₂ = -22 --> Subtract 5 from both sides
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 of a line segment, which is located exactly halfway between the two endpoints, can be calculated by taking the average of the x-values and the average of the y-values of the endpoints.
Let's denote the coordinates of endpoint V as (a, b). We know that the midpoint of UV is (5, -11), and the coordinates of endpoint U are (3, 5).
The midpoint of a line segment can be calculated using the following formulas:
Midpoint x-coordinate = (x-coordinate of U + x-coordinate of V) / 2
Midpoint y-coordinate = (y-coordinate of U + y-coordinate of V) / 2
Let's substitute the known values into these equations:
5 = (3 + a) / 2 -> 10 = 3 + a -> a = 7
-11 = (5 + b) / 2 -> -22 = 5 + b -> b = -27
Therefore, the coordinates of endpoint V are (7, -27).