Enter your answer and show all the steps that you use to solve this problem in the space provided. 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 are the average of the coordinates of the endpoints.
The midpoint formula:
Midpoint(x, y) = ((x1 + x2)/2, (y1 + y2)/2)
Given that the midpoint of UV¯¯¯¯¯ is (5, -11), and one endpoint is U(3, 5), let's substitute the values into the formula:
(5, -11) = ((3 + x)/2, (5 + y)/2)
Now, we can solve for x and y.
For x coordinate:
5 = (3 + x)/2
Multiply both sides by 2 to eliminate the fraction:
10 = 3 + x
Subtract 3 from both sides:
7 = x
For y coordinate:
-11 = (5 + y)/2
Multiply both sides by 2 to eliminate the fraction:
-22 = 5 + y
Subtract 5 from both sides:
-27 = y
Therefore, the coordinates of endpoint V are V(7, -27).
To find the coordinates of endpoint V, we can use the midpoint formula, which states that the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by the coordinates ((x₁ + x₂)/2, (y₁ + y₂)/2).
Given that the midpoint of UV¯¯¯¯¯ 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 assume the coordinates of endpoint V are (x, y).
Using the midpoint formula, we have:
((3 + x)/2, (5 + y)/2) = (5, -11)
Now we can equate the x and y-values separately:
(3 + x)/2 = 5
Simplifying the equation, we have:
3 + x = 10
x = 10 - 3
x = 7
For the y-values:
(5 + y)/2 = -11
Simplifying the equation, we have:
5 + y = -22
y = -22 - 5
y = -27
Therefore, the coordinates of endpoint V are (7, -27).
To find the coordinates of endpoint V, we can use the formula for the midpoint of a line segment.
The formula for the midpoint M of a line segment with endpoints (x1,y1) and (x2,y2) is:
M = ((x1+x2)/2, (y1+y2)/2)
Given that the midpoint M is (5,-11) and one endpoint U is (3,5), we can substitute these values into the formula to solve for the coordinates of endpoint V.
Using the formula, we have: