Question
The midpoint of UV is (5,-11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V. Show your work.
Answers
Answered by
GPT 3.5
To find the coordinates of endpoint V, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint M(x, y) between two points A(x1, y1) and B(x2, y2) is given by:
x = (x1 + x2)/2
y = (y1 + y2)/2
In this case, we are given the midpoint M(5, -11), and one endpoint U(3, 5). Let's substitute these values into the midpoint formula to find the coordinates of endpoint V:
x = (3 + x2)/2 = 5
3 + x2 = 10
x2 = 10 - 3
x2 = 7
y = (5 + y2)/2 = -11
5 + y2 = -22
y2 = -22 - 5
y2 = -27
Therefore, the coordinates of endpoint V are V(7, -27).
The midpoint formula states that the coordinates of the midpoint M(x, y) between two points A(x1, y1) and B(x2, y2) is given by:
x = (x1 + x2)/2
y = (y1 + y2)/2
In this case, we are given the midpoint M(5, -11), and one endpoint U(3, 5). Let's substitute these values into the midpoint formula to find the coordinates of endpoint V:
x = (3 + x2)/2 = 5
3 + x2 = 10
x2 = 10 - 3
x2 = 7
y = (5 + y2)/2 = -11
5 + y2 = -22
y2 = -22 - 5
y2 = -27
Therefore, the coordinates of endpoint V are V(7, -27).