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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 between two points (x₁, y₁) and (x₂, y₂) is given by:
(midpoint x-coordinate, midpoint y-coordinate) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, we are given the midpoint (5, -11) and one endpoint U(3, 5). Let's substitute these values into the midpoint formula and solve for the coordinates of endpoint V.
(x₁ + x₂)/2 = 5, where x₁ = 3
(3 + x₂)/2 = 5
3 + x₂ = 10
x₂ = 10 - 3
x₂ = 7
(y₁ + y₂)/2 = -11, where y₁ = 5
(5 + y₂)/2 = -11
5 + y₂ = -22
y₂ = -22 - 5
y₂ = -27
Therefore, the coordinates of endpoint V are V(7, -27).
To find the coordinates of endpoint V, we can use the formula for finding the midpoint of a line segment.
The midpoint formula is given by:
M = ( (x1+x2)/2 , (y1+y2)/2 )
Given that the midpoint is (5,-11) and one endpoint is U(3,5), we can substitute these values into the formula and solve for the coordinates of endpoint V.
Let's denote the coordinates of V as (x,y).
Using the midpoint formula:
(5,-11) = ( (3+x)/2 , (5+y)/2 )
We can now solve for x and y.
[(3+x)/2 = 5] [ (5+y)/2 = -11 ]
First, we can solve for x:
(3+x)/2 = 5
Multiply both sides by 2:
3+x = 10
Subtract 3 from both sides:
x = 7
Next, we can solve for y:
(5+y)/2 = -11
Multiply both sides by 2:
5 + y = -22
Subtract 5 from both sides:
y = -27
Therefore, the coordinates of endpoint V are (7,-27).