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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 of a line segment with endpoints (x1, y1) and (x2, y2) can be found by taking the average of the x-coordinates and the average of the y-coordinates.
Let's use this formula to find the coordinates of endpoint V.
The x-coordinate of the midpoint is given as 5, and we know that the x-coordinate of U is 3. So, the average of these two values will give us the x-coordinate of V:
(x1 + x2) / 2 = (3 + x2) / 2 = 5
Multiplying both sides by 2, we get:
3 + x2 = 10
Then, we subtract 3 from both sides:
x2 = 7
So, the x-coordinate of endpoint V is 7.
Similarly, the y-coordinate of the midpoint is given as -11, and we know that the y-coordinate of U is 5. So, the average of these two values will give us the y-coordinate of V:
(y1 + y2) / 2 = (5 + y2) / 2 = -11
Multiplying both sides by 2, we get:
5 + y2 = -22
Then, we subtract 5 from both sides:
y2 = -27
So, the y-coordinate of endpoint V is -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 with endpoints (x1, y1) and (x2, y2) is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In our case, we are given the midpoint (5, -11) and one endpoint U(3, 5). We need to find the coordinates of endpoint V.
Let's denote the coordinates of V as (x, y).
Using the midpoint formula, we can set up the following equation:
Midpoint = ((x1 + x) / 2, (y1 + y) / 2)
Substituting the given values, we have:
(5, -11) = ((3 + x) / 2, (5 + y) / 2)
To solve for x, let's isolate x in the equation:
2 * 5 = 3 + x
10 = 3 + x
Subtracting 3 from both sides:
10 - 3 = x
7 = x
So, the x-coordinate of endpoint V is 7.
Now, let's solve for y. We'll substitute x = 7 into the equation:
(5, -11) = ((3 + 7) / 2, (5 + y) / 2)
Simplifying, we have:
(5, -11) = (10 / 2, (5 + y) / 2)
(5, -11) = (5, (5 + y) / 2)
To solve for y, we'll isolate the variable y:
(5 + y) / 2 = -11
Multiplying both sides of the equation by 2:
5 + y = -22
Subtracting 5 from both sides:
y = -22 - 5
y = -27
So, the y-coordinate of endpoint V is -27.
Therefore, the coordinates of endpoint V are (7, -27).
To find the coordinates of endpoint V, we will use the midpoint formula.
The midpoint formula states that the coordinates of a midpoint (M) between two endpoints (A and B) can be found by taking the average of their x-coordinates and the average of their y-coordinates.
Given that the midpoint (M) is (5,-11) and one endpoint U is (3,5), we can use the midpoint formula to find the coordinates of endpoint V.
Let's denote the coordinates of endpoint V as (x,y).
Using the midpoint formula, we have:
x-coordinate of midpoint = (x-coordinate of U + x-coordinate of V)/2
=> 5 = (3 + x)/2
Solving for x, we get:
5 = (3 + x)/2
10 = 3 + x
10 - 3 = x
7 = x
Similarly, we can find the y-coordinate of endpoint V.
y-coordinate of midpoint = (y-coordinate of U + y-coordinate of V)/2
=> -11 = (5 + y)/2
Solving for y, we get:
-11 = (5 + y)/2
-22 = 5 + y
-22 - 5 = y
-27 = y
Therefore, the coordinates of endpoint V are (7, -27).