Question

Note: 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.

Answer 1

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).