Question

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 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).