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Question

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, (5, -11), are equal to the average of the coordinates of the two endpoints.

Let's call the coordinates of endpoint V (x, y).

Using the midpoint formula, we can set up the following equation:

[(3 + x)/2, (5 + y)/2] = (5, -11)

Now we can solve for x and y.

First, let's solve for x:
(3 + x)/2 = 5

Multiply both sides of the equation by 2:
3 + x = 10

Subtract 3 from both sides of the equation:
x = 7

Now let's solve for y:
(5 + y)/2 = -11

Multiply both sides of the equation by 2:
5 + y = -22

Subtract 5 from both sides of the equation:
y = -27

Therefore, the coordinates of endpoint V are (7, -27).