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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.
The midpoint formula states that the coordinates of the midpoint, (5, -11), are equal to the average of the coordinates of the two endpoints.
Let's call the coordinates of endpoint V (x, y).
Using the midpoint formula, we can set up the following equation:
[(3 + x)/2, (5 + y)/2] = (5, -11)
Now we can solve for x and y.
First, let's solve for x:
(3 + x)/2 = 5
Multiply both sides of the equation by 2:
3 + x = 10
Subtract 3 from both sides of the equation:
x = 7
Now let's solve for y:
(5 + y)/2 = -11
Multiply both sides of the equation by 2:
5 + y = -22
Subtract 5 from both sides of the equation:
y = -27
Therefore, the coordinates of endpoint V are (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 are the average of the coordinates of the two endpoints.
First, let's write down the coordinates of the midpoint and endpoint U:
Midpoint: (5, -11)
Endpoint U: (3, 5)
Next, we can use the midpoint formula to find the coordinates of endpoint V. The midpoint formula is:
(x₁ + x₂)/2, (y₁ + y₂)/2
Substituting the values:
(5, -11) = (3 + x₂)/2, (5 + y₂)/2
Now, let's solve for x₂:
(5, -11) = (3 + x₂)/2, (5 + y₂)/2
Multiply both sides of the equation by 2 to eliminate the fraction:
2 * (5, -11) = 2 * (3 + x₂)/2, 2 * (5 + y₂)/2
Simplifying:
(10, -22) = 3 + x₂, 5 + y₂
Subtract 3 from both sides of the equation to solve for x₂:
(10, -22) - 3 = 3 + x₂ - 3, 5 + y₂
Simplifying:
(7, -25) = x₂, 5 + y₂
Therefore, the coordinates of endpoint V are (7, -25).
To find the coordinates of endpoint V, we need to use the formula for finding the midpoint of a line segment.
The formula for finding the midpoint is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
We are given that the midpoint of UV is (5, -11) and one endpoint is U (3, 5). Let's plug these values into the formula to solve for the other endpoint V.
Let V be (xV, yV).
Using the formula for the midpoint:
(5, -11) = ((3 + xV)/2, (5 + yV)/2)
To extract xV and yV, multiply both sides of the equation by 2:
2 * (5, -11) = (3 + xV, 5 + yV)
Simplifying, we have:
(10, -22) = (3 + xV, 5 + yV)
Comparing the coordinates, we can equate them separately.
From the x-coordinates:
10 = 3 + xV
Subtracting 3 from both sides, we get:
xV = 10 - 3 = 7
From the y-coordinates:
-22 = 5 + yV
Subtracting 5 from both sides, we get:
yV = -22 - 5 = -27
Therefore, the coordinates of endpoint V are (7, -27).